Related papers: Reducedness of twisted loop groups

We classify (*)-subgroups of compact Lie groups of adjoint type, and associate a twisted root system to every (*)-subgroup. We study the structure of twisted root system in several aspects: properties of the small Weyl group W_{small} and…

This paper classifies the derivations of twisted group algebras in terms of the generators and defining relations of the group. In particular, we generalize some know results over group algebras to the case of twisted group algebras. We…

We introduce a technique for proving lower bounds on the essential dimension of split reductive groups. As an application, we strengthen the best previously known lower bounds for various split simple algebraic groups, most notably for the…

We propose and study a variation of the classical isomorphism problem for group rings in the context of projective representations. We formulate several weaker conditions following from our notion and give all logical connections between…

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

We calculate the twisted Reidemeister torsion of the complement of an iterated torus knot associated with a representation of its fundamental group to the complex special linear group of degree two. We also show that the twisted…

In an attempt to understand the origin of post groups introduced by C. Bai, L. Guo, Y. Sheng, R. Tang, from the perspective of rings, we introduce the notion of (weak) twisted post groups. First, we show that every element in a twisted post…

We construct Weil representations of twisted loop groups of type $A_n^{(2)}$ over local fields. We prove that the associated cover of the twisted loop group is the two fold metaplectic cover of the affine Kac-Moody group of type $A_n^{(2)}$…

Let $G\cong \mathbb Z/m_1\mathbb Z\times\ldots\times \mathbb Z/m_r\mathbb Z$ be a finite abelian group with $m_1\mid\ldots\mid m_r=\exp(G)$. The $n$-term subsums version of Kneser's Theorem, obtained either via the DeVos-Goddyn-Mohar…

We define twisted equivariant K-homology groups using geometric cycles. We compare them with approaches using Kasparov KK-Theory and (twisted) group C*-algebras.

We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems

For a field $K$ of characteristic different from 2, we find the explicit form of the minimal idempotents of the twisted group algebra $K_t< g>$ of a cyclic 2-group $<g>$ over $K$.

In this paper we compute the sharp lower bounds for the crossing number of $n$-string $k$-loop essential tangles. For essential tangles with only string components, we characterise the ones with the minimum crossing number for a given…

Let $G$ be the group of complex points of a real semi-simple Lie group whose fundamental rank is equal to 1, e.g. $G= \SL_2 (\C) \times \SL_2 (\C)$ or $\SL_3 (\C)$. Then the fundamental rank of $G$ is $2,$ and according to the conjecture…

Let $G$ be the quantum $GL_n$ over a field of characteristic $p\neq 0$. In this paper we define the ring of twisted tilting modules of $G$. We give generators and relations for the ring of twisted tilting modules of quantum $GL_2(k)$. We…

We prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n-1 generators tensor a cyclic group. We give a detailed description of the order of this cyclic group in terms of the…

We consider the problem of proving termination for triangular weakly non-linear loops (twn-loops) over some ring $\mathcal{S}$ like $\mathbb{Z}$, $\mathbb{Q}$, or $\mathbb{R}$. The guard of such a loop is an arbitrary quantifier-free…

We provide an easily verifiable condition for local $k$-connectedness of an inverse limit of polyhedra.

We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.

In this article we derive a simple twisted relative trace formula.