Related papers: A classification of spherical conjugacy classes in…

We extend the classical construction of operator colligations and characteristic functions. Consider the group $G$ of finite block unitary matrices of size $\alpha+\infty+...+\infty$ ($k$ times). Consider the subgroup $K=U(\infty)$, which…

It is well-known that special 2-groups can be described in terms of quadratic maps over fields of characteristic 2. In this article we develop methods to compute conjugacy classes, complex representations and characters of a real special…

The conjugacy problem in braid groups has been extensively studied, particularly from an algorithmic perspective. Established methods based on Garside structures, such as initial summit sets and super summit sets, provide effective…

We give the classification of elements - respectively cyclic subgroups - of finite order of the Cremona group, up to conjugation. Natural parametrisations of conjugacy classes, related to fixed curves of positive genus, are provided.

The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of…

Let $\F$ be an algebraically closed field. Let $\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\F$. Suppose the characteristic of $\F$ is \emph{large}, i.e. either zero or greater than…

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…

A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.

We classify subalgebras of the complex simple Lie algebra of type G2 up to conjugacy (by an inner automorphism).

Let G be a reductive connected group over the algebraic closure of a finite field. In this paper we give the classification of character sheaves on G in categorical terms (as a categorical centre). Previously such a classification was known…

The fine abelian group gradings on the simple exceptional classical Lie superalgebras over algebraically closed fields of characteristic 0 are determined up to equivalence.

Let $G$ be a simple complex classical group and $\g$ its Lie algebra. Let $\U_\hbar(\g)$ be the Drinfeld-Jimbo quantization of the universal enveloping algebra $\U(\g)$. We construct an explicit $\U_\hbar(\g)$-equivariant quantization of…

We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.

We prove that if a finite group $G$ contains a conjugacy class $K$ whose square is of the form $1 \cup D$, where $D$ is a conjugacy class of $G$, then $\langle K \rangle$ is a solvable proper normal subgroup of $G$ and we completely…

Let $X=G/H$ be a spherical variety over an algebraically closed field of characteristic $p\ge0$. We compute the $p'$-parts of $\pi_0(H)$ and $\pi_1(X)$ from the spherical system of $X$.

Let F be a field of characteristic not 2 and assume all algebras are over F. We establish several conjugacy theorems for the special linear Lie algebra sl_2 over an F-algebra which is a UFD. We find the structure of the full automorphism…

We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient…

Let G be a connected reductive algebraic group over an algebraic closed field. We define a (surjective) map from the set of conjugacy classes in the Weyl group to the set of unipotent classes of G.

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…