Related papers: Classification results for easy quantum groups

This is the fourth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of minus type.

We revise the enumeration of the imprimitive rank two quaternionic reflection groups, adding missing groups and establishing isomorphisms between groups in the published tables. The isomorphisms are obtained as a consequence of the…

We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…

This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…

In this paper we prove some general theorems about representations of finite groups arising from the inner semidirect product of groups. We show how these results can be used for standard applications of group theory in quantum chemistry…

We review known real forms of the quantum orthogonal groups SO_q(N). New *-conjugations are then introduced and we contruct all real forms of quantum orthogonal groups. We thus give an RTT formulation of the *-conjugations on SO_q(N) that…

We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from…

In this paper we inititate the study of abstract simplicial complexes which are initial segments of qualitative probability orders. This is a natural class that contains the threshold complexes and is contained in the shifted complexes, but…

For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central.…

We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…

We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the…

Given a discrete quantum group $H$ with a finite normal quantum subgroup $G$, we show that any positive, possibly unbounded, harmonic function on $H$ with respect to an irreducible invariant random walk is $G$-invariant. This implies that,…

Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

We prove that the quantum group inclusion $O_n \subset O_n^*$ is "maximal", where $O_n$ is the usual orthogonal group and $O_n^*$ is the half-liberated orthogonal quantum group, in the sense that there is no intermediate compact quantum…

The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…

We show that for every positive integer $n$ there exists a simple group that is of type $\mathrm{F}_{n-1}$ but not of type $\mathrm{F}_n$. For $n\ge 3$ these groups are the first known examples of this kind. They also provide infinitely…

We consider a special category of Hopf algebras, depending on parameters $\Sigma$ which possess properties similar to the category of representations of simple Lie group with highest weight $\lambda$. We connect quantum groups to minimal…

We determine all Lie groups compatible with the gauge structure of the Standard Elementary Particle Model (SM) and their representations. The groups are specified by congruence equations of quantum numbers. By comparison with the…

The construction of a quantum groupoid out of a double groupoid satisfying a filling condition and a perturbation datum is given. This extends previous work that appeared in math.QA/0308228. Several important classes of examples of tensor…