The Hochschild Cohomology Ring of Temperley–Lieb Algebras Revisited

We determine the Gerstenhaber algebra structure on the Hochschild cohomology ring of Temperley–Lieb algebras in this paper.

Hochschild cohomology of some quantum complete intersections

We compute the Hochschild cohomology ring of the algebras [Formula: see text] over a field [Formula: see text] where [Formula: see text] and where [Formula: see text] is a primitive [Formula: see text]th root of unity. We find the dimension of [Formula: see text] and show that it is independent of [Formula: see text]. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.

On Hochschild cohomology ring and integral cohomology ring for the semidihedral group

We will determine the ring structure of the Hochschild cohomology [Formula: see text] of the integral group ring of the semidihedral group [Formula: see text] of order [Formula: see text] for arbitrary integer [Formula: see text] by giving the precise description of the integral cohomology ring [Formula: see text] and by using a method similar to [T. Hayami, Hochschild cohomology ring of the integral group ring of the semidihedral [Formula: see text]-group, Algebra Colloq. 18 (2011) 241–258].

Cohomology rings of the plactic monoid algebra via a Gröbner–Shirshov basis

In this paper, we calculate the cohomology ring [Formula: see text] and the Hochschild cohomology ring of the plactic monoid algebra [Formula: see text] via the Anick resolution using a Gröbner–Shirshov basis.