Related papers: Singular blocks of restricted sl3
In this paper we study the homogenized algebra $B$ of the enveloping algebra $U$ of the Lie algebra sl(2,C). We look first to connections between the category of graded left $B$- modules and the category of $U$-modules, then we prove $B$ is…
We construct the nonlinear $W(sl(N+3),sl(3))$ algebras and find the spectrum of values of the central charge that gives rise, by contracting the $W(sl(N+3),sl(3))$ algebras, to a $W_3$ algebra belonging to the coset…
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we…
We classify blocks of categories of weight and generalized weight modules of algebras of twisted differential operators on P^n. Necessary and sufficient conditions for these blocks to be tame and proofs that some of the blocks are Koszul…
The symplectic blob algebra is a physically motivated quotient of the Hecke algebra $H(\tilde{C}_n)$ with a diagram calculus. We find the blocks for the symplectic blob algebra for all specialisations of its parameters over the complex…
We study the Lie module structure given by the Gerstenhaber bracket on the Hochschild cohomology groups of a monomial algebra with radical square zero. The description of such Lie module structure will be given in terms of the combinatorics…
The modular group algebra of an elementary abelian p-group is isomorphic to the restricted enveloping algebra of commutative restricted Lie algebra. The different ways of regarding this algebra result in different Hopf algebra structures…
In this paper, we find the Hochschild cohomology groups of the universal associative conformal envelope $U(3)$ of the Virasoro Lie conformal algebra with respect to associative locality $N=3$ on the generator with coefficients in all finite…
We develop the cohomology theory of color Lie superalgebras due to Scheunert--Zhang in a framework of nonhomogeneous quadratic Koszul algebras. In this approach, the Chevalley--Eilenberg complex of a color Lie algebra becomes a standard…
Several spectral sequence techniques are used in order to derive information about the structure of finite free resolutions of graded modules. These results cover estimates of the minimal number of generators of defining ideals of…
Soergel bimodules and their Hochschild homology are known to be important in the context of link homology. In this article we observe that Soergel bimodules may be naturally identified as the cohomology of well-defined objects in the…
We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer…
We study the restricted Verma modules of an affine Kac-Moody algebra at the critical level with special emphasis on their Jordan-H"older multiplicities. The Feigin-Frenkel conjecture gives a formula for these multiplicities that involves…
We present the Gerstenhaber algebra structure on the Hochschild cohomology of Koszul algebras defined by quivers and relations using the idea of homotopy liftings. E.L. Green, G. Hartman, E.N. Marcos and O. Solberg provided a canonical way…
In this paper, we compute the dimension of the Hochschild cohomology groups of any $m$-cluster tilted algebra of type $\tilde{\mathbb{A}}$. Moreover, we give conditions on the bounded quiver of an $m$-cluster tilted algebra $\Lambda$ of…
We formulate several basic properties of Verma supermodules over regular symmetrizable Kac--Moody Lie superalgebras, exhibiting $\mathfrak{gl}(1|1)$-nature as revealed through changing Borel subalgebras. We investigate variants of Verma…
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
In this paper, we compute the cohomology of the Heisenberg-Virasoro conformal algebra with coefficients in its modules, and in particular with trivial coefficients both for the basic and reduced complexes.
In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of…
We prove some results on the structure of certain classes of integral fusion categories and semisimple Hopf algebras under restrictions on the set of its irreducible degrees.