Related papers: Remark on Hopf images in quantum permutation group…

We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this algebra are indexed by set partitions. We show that there…

These are notes on seminal work of Freed, and subsequent developments, on the curvature properties of (Sobolev Lie) groups of maps from a Riemannian manifold into a compact Lie group. We are mainly interested in critical cases which are…

We study Hopf algebras via tools from geometric invariant theory. We show that all the invariants we get can be constructed using the integrals of the Hopf algebra and its dual together with the multiplication and the comultiplication, and…

We consider the `unstable Boardman map' (homomorphism if $k>0$) $$b:\pi^{m+k}\Sigma^k\Omega^lS^{n+l}\simeq[\Omega^lS^{n+l},\Omega^kS^{m+k}]\longrightarrow \mathrm{Hom}(H_*\Omega^lS^{n+l},H_*\Omega^kS^{m+k})$$ defined by $h(f)=f_*$. We work…

We show that the quantum automorphism group of the Clebsch graph is $SO_5^{-1}$. This answers a question by Banica, Bichon and Collins from 2007. More general for odd $n$, the quantum automorphism group of the folded $n$-cube graph is…

It can be shown that each permutation group $G \sqsubseteq S_n$ can be embedded, in a well defined sense, in a connected graph with $O(n+|G|)$ vertices. Some groups, however, require much fewer vertices. For instance, $S_n$ itself can be…

We construct a quantum version of the SU(2) Hopf bundle $S^7 \to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries…

We show that the Kac-Paljutkin Hopf algebra appears as a quotient of $C(SU_{-1}(2))$, which means that the corresponding quantum group $G_{KP}$ can be regarded as a quantum subgroup of $SU_{-1}(2)$. We combine the fact that corepresentation…

We show that the category of partial comodules over a Hopf algebra $H$ is comonadic over ${\sf Vect}_k$ and provide an explicit construction of this comonad using topological vector spaces. The case when $H$ is finite dimensional is treated…

Let $[\rho_{i_k},[\rho_{i_{k-1}},...,[\rho_{i_{1}}, \rho_{i_2}] ...]]$ be an iterated commutator of self-maps $\rho_{i_j} : \Sigma {\Bbb H}P^\infty \to \Sigma {\Bbb H}P^\infty, j = 1,2, ..., k$ on the suspension of the infinite quaternionic…

We describe the conjugacy classes of affine automorphisms in the group $Aut(n,\K)$ (respectively $Bir(\K^n)$) of automorphisms (respectively of birational maps) of $\K^n$. From this we deduce also the classification of conjugacy classes of…

This thesis is devoted to the study of Lie bialgebra and Hopf algebra structures related to certain versions of non-commutative geometry constructed on infinite-dimensional Lie algebras that arise in the context of asymptotic symmetries of…

We introduce the notion of characters of comodules over coribbon Hopf algebras. The case of quantum groups of type $A_n$ is studied. We establish a characteristic equation for the quantum matrix and a q-analogue of Harish-Chandra-…

For every odd prime $p$ and every integer $n\geq 12$ there is a Heisenberg group of order $p^{5n/4+O(1)}$ that has $p^{n^2/24+O(n)}$ pairwise nonisomorphic quotients of order $p^{n}$. Yet, these quotients are virtually indistinguishable.…

We study the coisotropic subgroup structure of standard SL_q(2,R) and the corresponding embeddable quantum homogeneous spaces. While the subgroups S^1 and R_+ survive undeformed in the quantization as coalgebras, we show that R is deformed…

The notion of a quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a…

Given a discrete quantum group A we construct a certain Hopf *-algebra AP which is a unital *-subalgebra of the multiplier algebra of A. The structure maps for AP are inherited from M(A) and thus the construction yields a compactification…

We study analytic continuations of quantum cohomology under simple flips $f: X \dashrightarrow X'$ along the extremal ray quantum variable $q^\ell$. The inverse correspondence $\Psi = [\Gamma_f]^*$ by the graph closure gives an embedding of…

Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct on A making it a multiplier Hopf algebra. In fact, because there exist integrals, we get an algebraic…

Piatetski-Shapiro the concept of CAP representations was introduced, elucidating the Saito-Kurokawa representations of $PGSp(4)$. In this paper we present a family of CAP representations for the group $Sp_{4n}(\mathbb A)$ through the…