Related papers: Unramified reductors of filtered and graded algebr…
We provide examples of finitely generated noetherian PI algebras for which there is no finite dimensional filtration with a noetherian associated graded ring; thus we answer negatively a question raised by M. Lorenz.
Quantum algebra of differential operators are studied
We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the…
The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.
We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are…
Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.
We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. Actually, the observations show there are two resources to get classification of filiform Leibniz algebras. The first of them…
The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frolicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a…
For a Dedekind domain $R$ with field of fractions $K$ a classical $R$-order in a semisimple $K$-algebra $A$ is an $R$-projective $R$-subalgebra $\Lambda$ of $A$ such that $K\Lambda=A$. We study differential graded $K$-algebras which are…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The…
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Fr\"olicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is…
We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.
The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…