Related papers: q-conjugacy classes in loop groups

We study twisted conjugacy classes of the unit element in different groups. Fel'shtyn and Troitsky showed that the twisted conjugacy class of the unit element of an abelian group is a subgroup for every automorphism. The structure is…

The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By…

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the…

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 classify the module categories over the double (possibly twisted) of a finite group.

We classify spherical conjugacy classes in a simple algebraic group over an algebraically closed field of good, odd characteristic.

In this paper we study twisted conjugacy classes and the $R_{\infty}$-property for classical linear groups. In particular, we prove that the general linear group ${\rm GL}_n(K)$ and the special linear group ${\rm SL}_n(K)$ possess…

We prove that Chevalley group over the field $F$ of zero characteristic possess $R_{\infty}$ property, if $F$ has torsion group of automorphisms or $F$ is an algebraically closed field which has finite transcendence degree over…

The problem of interpreting a set of ${\cal W}$-algebra constraints constructed in terms of an arbitrarily twisted scalar field as the recursion relations of a topological theory is addressed. In this picture, the conventional models of…

We show that the weighted fusion category algebra of the principal 2-block $b_0$ of $\mathrm{GL}_2(q)$ is the quotient of the $q$-Schur algebra $\mathcal{S}_2(q)$ by its socle, for $q$ an odd prime power. As a consequence, we get a…

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form…

We introduce a representation theory of q-Lie algebras defined earlier in \cite{DG1}, \cite{DG2}, formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in…

We give a general construction for right conjugacy closed loops, using $GL(2,q)$ for $q$ a prime power. Under certain conditions, the loops constructed are simple, giving the first general construction for finite, simple right conjugacy…

We construct two practical algorithms for twisted conjugacy classes of polycyclic-by-finite groups. The first algorithm determines whether two elements of a group are twisted conjugate for two given endomorphisms, under the condition that…

As part of our study of the $q$-tetrahedron algebra $\boxtimes_q$ we introduce the notion of a $q$-inverting pair. Roughly speaking, this is a pair of invertible semisimple linear transformations on a finite-dimensional vector space, each…

Let $Q$ be a conjugacy closed loop, and $N(Q)$ its nucleus. Then $Z(N(Q))$ contains all associators of elements of $Q$. If in addition $Q$ is diassociative (i.e., an extra loop), then all these associators have order 2. If $Q$ is…

We use the fusion construction in the twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a byproduct we uniformly realize all non-spin fundamental modules for quantized…

Let $E:y^2=x^3+ax+b$ be an elliptic curve defined over $\mathbb{Q}$. We compute certain twists of the classical modular curves $X(8)$. Searching for rational points on these twists enables us to find non-trivial pairs of $8$-congruent…

Let G be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level k fusion ring R_k(G) of G with the twisted equivariant K-homology at level k+h, where h is the dual Coxeter number. In this…