scholarly journals ALGEBRAS ASSOCIATED TO PSEUDO-ROOTS OF NONCOMMUTATIVE POLYNOMIALS ARE KOSZUL

2005 ◽  
Vol 15 (04) ◽  
pp. 643-648 ◽  
Author(s):  
DMITRI PIONTKOVSKI
Keyword(s):  
Hilbert Series ◽  
Necessary Condition ◽  
Quadratic Algebras ◽  
Noncommutative Polynomials

Quadratic algebras associated to pseudo-roots of noncommutative polynomials have been introduced by I. Gelfand, Retakh, and Wilson in connection with studying the decompositions of noncommutative polynomials. Later they (with S. Gelfand and Serconek) showed that the Hilbert series of these algebras and their quadratic duals satisfy the necessary condition for Koszulity. It is proved in this note that these algebras are Koszul.

scholarly journals Hilbert series of quadratic algebras associated with pseudo-roots of noncommutative polynomials

2002 ◽  
Vol 254 (2) ◽  
pp. 279-299 ◽  
Author(s):  
Israel Gelfand ◽  
Sergei Gelfand ◽  
Vladimir Retakh ◽  
Shirlei Serconek ◽  
Robert Lee Wilson
Keyword(s):  
Hilbert Series ◽  
Quadratic Algebras ◽  
Noncommutative Polynomials

Families of quadratic algebras and Hilbert series

2005 ◽  
pp. 119-131
Author(s):  
Alexander Polishchuk ◽  
Leonid Positselski
Keyword(s):  
Hilbert Series ◽  
Quadratic Algebras

scholarly journals The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture

2011 ◽  
Vol 141 (3) ◽  
pp. 609-629 ◽  
Author(s):  
Natalia Iyudu ◽  
Stanislav Shkarin
Keyword(s):  
Commutative Algebra ◽  
Hilbert Series ◽  
Infinite Field ◽  
Asymptotic Results ◽  
Quadratic Algebras ◽  
Princeton University ◽  
Number Of Generators ◽  
Finite Dimensional ◽  
Generic Algebra ◽  
Generic Algebras

We study the question of whether the famous Golod-Shafarevich estimate, which gives a lower bound for the Hilbert series of a (non-commutative) algebra, is attained. This question was considered by Anick in his 1983 paper, ‘Generic algebras and CW-complexes’ (Princeton University Press), where he proved that the estimate is attained for the number of quadratic relations d ≤ ¼n2 and d ≥ ½n2, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to ½n(n – 1) was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional.We prove that over any infinite field, the Anick conjecture holds for d ≥ (n2 + n) and an arbitrary number of generators n, and confirm the Vershik conjecture over any field of characteristic 0. We give also a series of related asymptotic results.

scholarly journals PBW Property for Associative Universal Enveloping Algebras Over an Operad

2020 ◽  
Author(s):  
Anton Khoroshkin
Keyword(s):  
Associative Algebra ◽  
Hilbert Series ◽  
Abelian Category ◽  
Universal Enveloping Algebra ◽  
Necessary Condition ◽  
Grobner Basis ◽  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Category Of Modules

Abstract Given a symmetric operad $\mathcal{P}$ and a $\mathcal{P}$-algebra $V$, the associative universal enveloping algebra ${\textsf{U}_{\mathcal{P}}}$ is an associative algebra whose category of modules is isomorphic to the abelian category of $V$-modules. We study the notion of PBW property for universal enveloping algebras over an operad. In case $\mathcal{P}$ is Koszul a criterion for the PBW property is found. A necessary condition on the Hilbert series for $\mathcal{P}$ is discovered. Moreover, given any symmetric operad $\mathcal{P}$, together with a Gröbner basis $G$, a condition is given in terms of the structure of the underlying trees associated with leading monomials of $G$, sufficient for the PBW property to hold. Examples are provided.

The Infancy of Solar-Type Stars and its Relevance for the Origin of Life

1997 ◽  
Vol 161 ◽  
pp. 267-282 ◽  
Author(s):  
Thierry Montmerle
Keyword(s):  
Main Sequence ◽  
Solar Nebula ◽  
Circumstellar Disks ◽  
T Tauri Stars ◽  
Necessary Condition ◽  
Sequence Evolution ◽  
T Tauri ◽  
Solar Type ◽  
Optical Domain ◽  
The Origin Of Life

AbstractFor life to develop, planets are a necessary condition. Likewise, for planets to form, stars must be surrounded by circumstellar disks, at least some time during their pre-main sequence evolution. Much progress has been made recently in the study of young solar-like stars. In the optical domain, these stars are known as «T Tauri stars». A significant number show IR excess, and other phenomena indirectly suggesting the presence of circumstellar disks. The current wisdom is that there is an evolutionary sequence from protostars to T Tauri stars. This sequence is characterized by the initial presence of disks, with lifetimes ~ 1-10 Myr after the intial collapse of a dense envelope having given birth to a star. While they are present, about 30% of the disks have masses larger than the minimum solar nebula. Their disappearance may correspond to the growth of dust grains, followed by planetesimal and planet formation, but this is not yet demonstrated.

Universal ESEM

1993 ◽  
Vol 51 ◽  
pp. 786-787
Author(s):  
G.D. Danilatos
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
High Vacuum ◽  
Natural Extension ◽  
Necessary Condition ◽  
Environmental Scanning ◽  
Detection Systems ◽  
Small Gain ◽  
Detection Medium ◽  
Scanning Electron

The environmental scanning electron microscope (ESEM) has evolved as the natural extension of the scanning electron microscope (SEM), both historically and technologically. ESEM allows the introduction of a gaseous environment in the specimen chamber, whereas SEM operates in vacuum. One of the detection systems in ESEM, namely, the gaseous detection device (GDD) is based on the presence of gas as a detection medium. This might be interpreted as a necessary condition for the ESEM to remain operational and, hence, one might have to change instruments for operation at low or high vacuum. Initially, we may maintain the presence of a conventional secondary electron (E-T) detector in a "stand-by" position to switch on when the vacuum becomes satisfactory for its operation. However, the "rough" or "low vacuum" range of pressure may still be considered as inaccessible by both the GDD and the E-T detector, because the former has presumably very small gain and the latter still breaks down.

Analysis of interconnections between technical systems on hierarchically connected technological levels of steel sheet production by hot rolling

2020 ◽  
Vol 76 (8) ◽  
pp. 847-855
Author(s):  
E. N. Shiryaeva ◽  
M. A. Polyakov ◽  
D. V. Terent'ev
Keyword(s):  
Hot Rolling ◽  
Systems Analysis ◽  
Rolling Mill ◽  
Steel Sheet ◽  
Technological System ◽  
Necessary Condition ◽  
Rolled Sheet ◽  
Technological Systems ◽  
Hot Rolling Mill ◽  
Technical Systems

Complexity of modern metallurgical plants, presence of great number of horizontal and vertical interactions between their various structural subdivisions makes it necessary to apply a systems analysis to elaborate effective measures for stable development of a plant operation. Among such measures, digitalization of a plant is widespread at present. To implement the digitalization it is necessary to have clear vision about links at all the levels of the technological system of a plant. A terminology quoted, accepted in the existing regulatory documents for defining of conceptions, comprising the technological system. It was shown, that the following four hierarchical levels of technological systems are distinguished: technological systems of operations, technological systems of processes, technological systems of production subdivisions and technological systems of plants. A hierarchical scheme of technological systems of hot-rolled sheet production at an integrated steel plant presented. Existing horizontal and vertical links between the basic plant’s shops shown. Peculiarities of flows of material, energy and information at the operation “rolling” of the technological system “hot rolling of a steel sheet” considered. As a technical system of the technological process of the hot rolling, the hot rolling mill was chosen. A structural diagram of the hot rolling mill was elaborated, the mill being consisted of reheating furnaces, roughing and finishing stand groups, with an intermediate roll-table between them, and down-coilers section. Since the rolling stands are the basic structural elements of the hot rolling mill, structural diagrams of a roughing and a finishing stands were elaborated. Results of the systems analysis of the technological and technical systems, hierarchically linked in the process of steel sheet hot rolling, can be applied for perfection of organization structure of the whole plant, as well as for elaboration mathematical models of a system separate elements functioning, which is a necessary condition for a plant digitalization.

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