scholarly journals Module and Hochschild cohomology of certain semigroup algebras

2015 ◽  
Vol 49 (4) ◽  
pp. 315-318
Author(s):  
A. Shirinkalam ◽  
A. Pourabbas ◽  
M. Amini
Keyword(s):  
Hochschild Cohomology ◽  
Semigroup Algebras

scholarly journals The equality of Hochschild cohomology group and module cohomology group for semigroup algebras

2022 ◽  
Vol 40 ◽  
pp. 1-9
Author(s):  
Ebrahim Nasrabadi
Keyword(s):  
Inverse Semigroup ◽  
Cohomology Group ◽  
Hochschild Cohomology ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Hochschild Cohomology Group

‎Let $S$ be a commutative inverse semigroup with idempotent set $E$‎. ‎In this paper‎, ‎we show that for every $n\in \mathbb{N}_0$‎, ‎$n$-th Hochschild cohomology group of semigroup algebra $\ell^1(S)$ with coefficients in $\ell^\infty(S)$ and its $n$-th $\ell^1(E)$-module cohomology group‎, ‎are equal‎. ‎Indeed‎, ‎we prove that‎ ‎\[ \HH^{n}(\ell^1(S),\ell^\infty(S))=\HH^{n}_{\ell^1(E)}(\ell^1(S),\ell^\infty(S)),\] for all $n\geq 0$‎.

Spectra in Some Inverse Semigroup Algebras

2004 ◽  
Vol 104 (2) ◽  
pp. 211-218 ◽  
Author(s):  
M. J. Crabb ◽  
J. Duncan ◽  
C. M. McGregor
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebras

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals Homological dimension in semigroup algebras

1971 ◽  
Vol 18 (3) ◽  
pp. 404-413 ◽  
Author(s):  
William R Nico
Keyword(s):  
Homological Dimension ◽  
Semigroup Algebras

scholarly journals The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras

2021 ◽  
Vol 580 ◽  
pp. 264-298
Author(s):  
Joanna Meinel ◽  
Van C. Nguyen ◽  
Bregje Pauwels ◽  
María Julia Redondo ◽  
Andrea Solotar
Keyword(s):  
Hochschild Cohomology ◽  
Special Biserial Algebras

scholarly journals Going from cohomology to Hochschild cohomology

2005 ◽  
Vol 288 (2) ◽  
pp. 263-278 ◽  
Author(s):  
Emil Sköldberg
Keyword(s):  
Hochschild Cohomology

scholarly journals Gerstenhaber brackets on Hochschild cohomology of twisted tensor products

2017 ◽  
Vol 11 (4) ◽  
pp. 1351-1379 ◽  
Author(s):  
Lauren Grimley ◽  
Van Nguyen ◽  
Sarah Witherspoon
Keyword(s):  
Hochschild Cohomology ◽  
Tensor Products
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