Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHochschild cohomology of triangular string algebras and its ring structure
275
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We compute the Hochschild cohomology groups $HH^*(A)$ in case $A$ is a triangular string algebra, and show that its ring structure is trivial.
rate research
Read More
We give a complete study of the Clifford-Weyl algebra ${mathcal C}(n,2k)$ from Bose-Fermi statistics, including Hochschild cohomology (with coefficients in itself). We show that ${mathcal C}(n,2k)$ is rigid when $n$ is even or when $k eq 1$. We find all non-trivial deformations of ${mathcal C}(2n+1,2)$ and study their representations.
The Hochschild cohomology ring of a group algebra is an object that has received recent attention, but is difficult to compute, in even the simplest of cases. In this paper, we use the product formula due to Witherspoon and Siegel to extend some of their computations. In particular, we compute the Hochschild cohomology algebra of group algebras kG where |G| is less than 16, and we provide an alternative computation of the ring $HH^*(k(E ltimes P))$ considered by Kessar and Linckelmann.
We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH*$(A)$ when $A$ is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdells resolution and we describe generators of these groups. Then we construct comparison morphisms between the bar resolution and Bardzells resolution in order to get formulae for the cup product and the Lie bracket. We find conditions on the bound quiver associated to string algebras in order to get non-trivial structures.
We show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby we obtain a number of positive characteristic stable invariants, such as the $p$-toral rank of $mathrm{HH}^1(A,A)$. We also prove a more general result concerning Iwanaga-Gorenstein algebras, using a more general notion of stable equivalences of Morita type. Several applications are given to commutative algebra and modular representation theory. These results are proven by first establishing the stable invariance of the $B_infty$-structure of the Hochschild cochain complex. In the appendix we explain how the $p$-power operation on Hochschild cohomology can be seen as an artifact of this $B_infty$-structure. In particular, we establish well-definedness of the $p$-power operation, following some -- originally topological -- methods due to May, Cohen and Turchin, using the language of operads.
Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
