scholarly journals Silting and Tilting for Weakly Symmetric Algebras

2021 ◽  
Author(s):  
Jenny August ◽  
Alex Dugas
Keyword(s):  
Symmetric Algebra ◽  
The Other ◽  
Symmetric Algebras ◽  
Finite Dimensional ◽  
Other Hand ◽  
Weakly Symmetric

AbstractIf A is a finite-dimensional symmetric algebra, then it is well-known that the only silting complexes in Kb(projA) are the tilting complexes. In this note we investigate to what extent the same can be said for weakly symmetric algebras. On one hand, we show that this holds for all tilting-discrete weakly symmetric algebras. In particular, a tilting-discrete weakly symmetric algebra is also silting-discrete. On the other hand, we also construct an example of a weakly symmetric algebra with silting complexes that are not tilting.

scholarly journals Integrable lifts for transitive Lie algebroids

2018 ◽  
Vol 29 (09) ◽  
pp. 1850062 ◽  
Author(s):  
Iakovos Androulidakis ◽  
Paolo Antonini
Keyword(s):  
Extra Dimensions ◽  
Lie Algebroids ◽  
The Other ◽  
Lie Algebroid ◽  
Base Manifold ◽  
Lie Groupoid ◽  
Finite Dimensional ◽  
Other Hand ◽  
De Rham ◽  
Simply Connected

Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid is the quotient of a finite-dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an “Almeida–Molino” integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a “de Rham” integrable lift for any given transitive Abelian Lie algebroid.

scholarly journals Primary decomposition in enveloping algebras

1981 ◽  
Vol 24 (2) ◽  
pp. 83-85 ◽  
Author(s):  
K. A. Brown ◽  
T. H. Lenagan
Keyword(s):  
Lie Algebra ◽  
Universal Enveloping Algebra ◽  
The Other ◽  
Primary Decomposition ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Factor Ring ◽  
Finite Dimensional ◽  
Other Hand

Recently, the first author and, independently, A. V. Jategaonkar have shown that every factor ring of U(g), the universal enveloping algebra of a finite dimensional complex Lie algebra, has a primary decomposition if g is solvable and almost algebraic. On the other hand, a suitable factor ring of U(SL(2, ℂ) fails to have a primary decomposition (1).

scholarly journals Some Remarks on Symmetric and Frobenius Algebras

1960 ◽  
Vol 16 ◽  
pp. 65-71 ◽  
Author(s):  
J. P. Jans
Keyword(s):  
Vector Space ◽  
Space Dimension ◽  
Symmetric Algebra ◽  
Dimensional Case ◽  
Infinite Dimensional ◽  
Symmetric Algebras ◽  
Finite Dimensional ◽  
Frobenius Algebras ◽  
Finite Dimensional Case

In [5] we defined the concepts of Frobenius and symmetric algebra for algebras of infinite vector space dimension over a field. It was shown there that with the introduction of a topology and the judicious use of the terms continuous and closed, many of the classical theorems of Nakayama [7, 8] on Frobenius and symmetric algebras could be generalized to the infinite dimensional case. In this paper we shall be concerned with showing certain algebras are (or are not) Frobenius or symmetric. In Section 3, we shall see that an algebra can be symmetric or Frobenius in “many ways”. This is a problem which did not arise in the finite dimensional case.

Invertibility and Class Number of Orders

1971 ◽  
Vol 23 (1) ◽  
pp. 1-11
Author(s):  
Howard Gorman
Keyword(s):  
Class Number ◽  
Symmetric Algebra ◽  
Preliminary Results ◽  
Symmetric Algebras ◽  
Finite Dimensional ◽  
Valuation Rings ◽  
Work Done ◽  
Equivalent Conditions

This paper continues the work begun in [5] and concerns the invertibility of modules in a finite-dimensional, symmetric algebra L with 1 over a field. In particular, we continue the work done in [5] which dealt with the connection between invertibility in these algebras and a condition called the Brandt Condition, which is a reformulation by Kaplansky [6] of some ideas of Brandt.We begin by proving some preliminary results on invertibility and some equivalent conditions for the dual of an order to be principal.Then, we define the class number of an order and reformulate the concept of invertibility in terms of class number. In this terminology, we find some equivalent conditions which ensure that an order in certain algebras L (including commutative, symmetric algebras, and algebras with a strong involution) has class number equal to 1 (i.e., all modules principal), and we characterize a class of Brandt algebras over the quotient fields of valuation rings as those in which all orders have class number less than or equal to 2.

scholarly journals EXT-FINITE MODULES FOR WEAKLY SYMMETRIC ALGEBRAS WITH RADICAL CUBE ZERO

2016 ◽  
Vol 102 (1) ◽  
pp. 108-121 ◽  
Author(s):  
KARIN ERDMANN
Keyword(s):  
Complete Classification ◽  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Finite Generation ◽  
Symmetric Algebras ◽  
Finite Dimensional ◽  
Wild Representation Type ◽  
Weakly Symmetric ◽  
Support Varieties

Assume that $A$ is a finite-dimensional algebra over some field, and assume that $A$ is weakly symmetric and indecomposable, with radical cube zero and radical square nonzero. We show that such an algebra of wild representation type does not have a nonprojective module $M$ whose ext-algebra is finite dimensional. This gives a complete classification of weakly symmetric indecomposable algebras which have a nonprojective module whose ext-algebra is finite dimensional. This shows in particular that existence of ext-finite nonprojective modules is not equivalent with the failure of the finite generation condition (Fg), which ensures that modules have support varieties.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

Can the Academic Self-Concept be Positive and Realistic?

2005 ◽  
Vol 19 (3) ◽  
pp. 129-132 ◽  
Author(s):  
Reimer Kornmann
Keyword(s):  
Academic Performance ◽  
Opposite Effect ◽  
Self Esteem ◽  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
High Ability ◽  
Self Image ◽  
Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

Stories and the Self

2020 ◽  
Vol 32 (2) ◽  
pp. 47-58 ◽  
Author(s):  
Stefan Krause ◽  
Markus Appel
Keyword(s):  
Meta Analysis ◽  
The Self ◽  
The Other ◽  
Lower Degree ◽  
Contrast Effects ◽  
Self Perception ◽  
Self Perceptions ◽  
Other Hand ◽  
The One ◽  
Implicit And Explicit

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.

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