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A little bit of extra functoriality for Ext and the computation of the Gerstenhaber bracket
(Elsevier Science, 2017-08)
We show that the action of the Lie algebra HH1(A) of outer derivations of an associative algebra A on the Hochschild cohomology HH•(A) of A given by the Gerstenhaber bracket can be computed in terms of an arbitrary projective ...
The gerstenhaber bracket in hochschild cohomology: methods and examples
(American Mathematical Society, 2020-11)
Homological methods provide important information about the structureof associative algebras, revealing sometimes hidden connections amongst them. Thistext is about the Gerstenhaber bracket in Hochschild cohomology of ...
Gerstenhaber Algebra Structure on the Hochschild Cohomology of Quadratic String Algebras
(Springer, 2018-02-26)
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 Barzdell’s resolution and we describe generators ...
Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra
(European Mathematical Society, 2021-12-07)
For each nonzero h ∈ F[x], where F is a field, let Ah be the unital associative algebra generated by elements x; y, satisfying the relation yx - xy = h. This gives a parametric family of subalgebras of the Weyl algebra A1, ...
Homological invariants relating the super Jordan plane to the Virasoro algebra
(Academic Press Inc Elsevier Science, 2018-08)
Nichols algebras are an important tool for the classification of Hopf algebras. Within those with finite GK dimension, we study homological invariants of the super Jordan plane, that is, the Nichols algebra A=B(V(−1,2)). ...
On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras
(Academic Press Inc Elsevier Science, 2020-09)
In this paper we determine the first Hochschild homology and cohomology with different coefficients for gentle algebras and we give a geometrical interpretation of these (co)homologies using the ribbon graph of a gentle ...