Related papers: Gradings on composition superalgebras
We categorify the Hecke algebra with parameters 1 and v using a variation of the category of Soergel bimodules.
Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We…
Let $R$ be a finite-dimensional algebra over an algebraically closed field $F$ graded by an arbitrary group $G$. We prove that $R$ is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite…
It is known that there are Lie algebras with non-semigroup gradings, i.e. such that the binary operation on the grading set is not associative. We provide a similar example in the class of associative algebras.
Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
We generalise to a group homomorphism $\tau$ the $\chi$-graded categories of S\"{o}zer and Virelizier. These are categories in which both morphisms and objects have compatible degrees. We give a 'half-enriched' Yoneda lemma, a structure…
Let P a locally finite partially ordered set, F a field, G a group, and I(P,F) the incidence algebra of P over F. We describe all the inequivalent elementary G-gradings on this algebra. If P is bounded, F is a infinite field of…
There are three kinds of Lie superalgebras for each differentiable manifold. In this note, we shall show an application of the homology groups of those superalgebras in order to classify 4 dimensional Engel-like Lie algebras.
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics.…
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras
A subalgebra S of a Leibniz algebra L is called self-idealizing in L if it coincides with its idealizer IL(S). In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing.
We classify the algebraic combinatorial geometries of arbitrary field extensions of transcendence degree greater than 4 and describe their groups of automorphisms. Our results and proofs extend similar results and proofs by Evans and…
Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$…
We investigate the notion of associated graded coalgebra (algebra) of a bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize those which are bialgebras of type one in the framework of abelian braided monoidal…
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
In this paper, Lie conformal superalgebras of rank (2 + 1) are completely classified (up to isomorphism) and their automorphism groups are determined. Furthermore, we give the classification of the finite irreducible conformal modules over…