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In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…

A class of Cantor-type spaces and related geometric structures are discussed.

This work extends the theory of reciprocal diagrams in graphic statics to frameworks that are invariant under finite group actions by utilizing the homology and representation theory of cellular cosheaves, recent tools from applied…

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large…

We study a finite-dimensional quotient of the Hecke algebra of type $H_n$ for general $n$, using a calculus of diagrams. This provides a basis of monomials in a certain set of generators. Using this, we prove a conjecture of C.K. Fan about…

Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…

We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion…

We interpret a result of S. Oehms as a statement about the symplectic ideal. We use this result to prove a double centraliser theorem for the symplectic group acting on \bigoplus_{r=0}^s\otimes^rV, where V is the natural module for the…

This paper is concerned with the completion of the proof of the Bergman centralizer theorem by using generic matrices based on our previous quantization proof \cite{KBRZh}. Additionally, we establish that the algebra of generic matrices…

We find a recursive algorithm for computing the precise centralizers of the complex orthogonal and symplectic groups, and hence the isotropy groups, with respect to the similarity transformation on the spaces of skew-symmetric and…

We present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero-Moser spaces and rational Cherednik algebras associated to complex reflection groups. Especially, we are concerned with…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require…

We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures…

We study the algebra ${\cal A}_n$ and the basis of the Hilbert space ${\cal H}_n$ in terms of the $\theta$ functions of the positions of $n$ solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation…

Berenstein, Fomin and Zelevinsky defined functions on double Bruhat cells which they called generalized minors. By relating certain double Bruhat cells to configuration spaces of flags, we give formulas for these generalized minors as…

In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…

This paper describes the centers of the universal enveloping algebras and the invariant rings of the standard filiform Lie algebras over fields of characteristic zero and also over large enough prime characteristic. We determine explicit…