The first cohomology group of trivial extensions of special biserial algebras

2004 ◽  
Vol 47 (4) ◽  
pp. 578 ◽  
Author(s):  
Yunge XU
Keyword(s):  
Cohomology Group ◽  
Special Biserial Algebras ◽  
First Cohomology Group

Derivations and Automorphism Group of Completed Witt Lie Algebra

2012 ◽  
Vol 19 (03) ◽  
pp. 581-590 ◽  
Author(s):  
Yongping Wu ◽  
Ying Xu ◽  
Lamei Yuan
Keyword(s):  
Finite Element ◽  
Automorphism Group ◽  
Lie Algebra ◽  
Cohomology Group ◽  
Locally Finite ◽  
Simple Lie Algebra ◽  
Derivation Algebra ◽  
First Cohomology Group

In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a by-product, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad -locally finite element.

scholarly journals On the Monodromy of Milnor Fibers of Hyperplane Arrangements

2014 ◽  
Vol 57 (4) ◽  
pp. 697-707 ◽  
Author(s):  
Pauline Bailet
Keyword(s):  
Cohomology Group ◽  
Hyperplane Arrangement ◽  
General Setting ◽  
Hyperplane Arrangements ◽  
Milnor Fiber ◽  
First Cohomology Group

AbstractWe describe a general setting where the monodromy action on the first cohomology group of the Milnor fiber of a hyperplane arrangement is the identity.

scholarly journals Group Cohomology and Lp-Cohomology of Finitely Generated Groups

2003 ◽  
Vol 46 (2) ◽  
pp. 268-276 ◽  
Author(s):  
Michael J. Puls
Keyword(s):  
Banach Space ◽  
Cohomology Group ◽  
Nilpotent Groups ◽  
Group Cohomology ◽  
Infinite Group ◽  
Finitely Generated ◽  
Finitely Generated Groups ◽  
Cohomology Space ◽  
First Cohomology Group

AbstractLet G be a finitely generated, infinite group, let p > 1, and let Lp(G) denote the Banach space . In this paper we will study the first cohomology group of G with coefficients in Lp(G), and the first reduced Lp-cohomology space of G. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.

THE FIRST COHOMOLOGY GROUP OF BANACH INVERSE SEMIGROUP ALGEBRAS WITH COEFFICIENTS IN -EMBEDDED BANACH BIMODULES

2019 ◽  
Vol 101 (3) ◽  
pp. 488-495
Author(s):  
HOGER GHAHRAMANI
Keyword(s):  
Banach Space ◽  
Inverse Semigroup ◽  
Cohomology Group ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Mild Conditions ◽  
First Cohomology Group

Let $S$ be a discrete inverse semigroup, $l^{1}(S)$ the Banach semigroup algebra on $S$ and $\mathbb{X}$ a Banach $l^{1}(S)$-bimodule which is an $L$-embedded Banach space. We show that under some mild conditions ${\mathcal{H}}^{1}(l^{1}(S),\mathbb{X})=0$. We also provide an application of the main result.

The first cohomology group of leaves and local stability of compact foliations

1982 ◽  
Vol 37 (2) ◽  
pp. 229-267 ◽  
Author(s):  
Elmar Vogt
Keyword(s):  
Cohomology Group ◽  
Local Stability ◽  
First Cohomology Group

scholarly journals THE FIRST COHOMOLOGY GROUP OF THE TRIVIAL EXTENSION OF A MONOMIAL ALGEBRA

2004 ◽  
Vol 03 (02) ◽  
pp. 143-159 ◽  
Author(s):  
CLAUDE CIBILS ◽  
MARÍA JULIA REDONDO ◽  
MANUEL SAORÍN
Keyword(s):  
Cohomology Group ◽  
Hochschild Cohomology ◽  
Trivial Extension ◽  
Monomial Algebra ◽  
Finite Dimensional ◽  
Hochschild Cohomology Group ◽  
First Cohomology Group

Given a finite-dimensional monomial algebra A, we consider the trivial extension TA and provide formulae, depending on the characteristic of the field, for the dimensions of the summands HH1(A) and Alt (DA) of the first Hochschild cohomology group HH1(TA). From these a formula for the dimension of HH1(TA) can be derived.

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