Related papers: Quasireductive supergroups
We present some fundamental results on (possibly nonlinear) algebraic semigroups and monoids. These include a version of Chevalley's structure theorem for irreducible algebraic monoids, and the description of all algebraic semigroup…
In this paper, we study a special class of quasi-homomorphisms, i.e. quasi-retractions from a group to its subgroups. We first give some algebraic and geometric properties of quasi-retracts and then propose a theory of quasi-split short…
We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.
A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…
A toroidal affine Nash group is the affine Nash group analogue of an anti-affine algebraic group. In this note, we prove analogues of Rosenlicht's structure and decomposition theorems: (1) Every affine Nash group $G$ has a smallest normal…
We introduce a category of $q$-oscillator representations over the quantum affine superalgebras of type $D$ and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these…
A finite quantum hypergroup is a finite-dimensional unital algebra $A$ over the field of complex numbers. There is a coproduct on $A$, a coassociative map from $A$ to $A\otimes A$ assumed to be unital, but it is not required to be an…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
It is shown that a separable C*-algebra is inner quasidiagonal if and only if it has a separating family of quasidiagonal irreducible representations. As a consequence, a separable C*-algebra is a strong NF algebra if and only if it is…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
We provide the spherical systems of the wonderful reductive subgroups of any reductive group.
Fusion is defined for arbitrary lowest weight representations of $W$-algebras, without assuming rationality. Explicit algorithms are given. A category of quasirational representations is defined and shown to be stable under fusion.…
We consider numerical semigroups associated with normal weighted homogeneous surface singularities with rational homology sphere links. We say that a semigroup is representable if it can be realized in this way. In this article, we study…
A word hyperbolic group $G$ is called GFERF if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it. We show that in any such group, the product of finitely many quasiconvex subgroups is closed…
A special linear Lie group over the real number field and the quarternion field admits a projectivley flat affine connection. We show that parabolic subgroups are autoparallel submanifolds and give a criterion the induced connection is…
We impose a rather unknown algebraic structure called a `hyperstructure' to the underlying space of an affine algebraic group scheme. This algebraic structure generalizes the classical group structure and is canonically defined by the…
For the coordinate algebras of connected affine algebraic groups, we explore the problem of finding a presentation by generators and relations canonically determined by the group structure.