Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2109.04071

Presentations of projective quantum groups

Daniel Gromada
View original source ↗Read source document ↗Export metadata ↓

Abstract

Given an orthogonal compact matrix quantum group defined by intertwiner relations, we characterize by relations its projective version. As a sample application, we prove that $PU_n^+=PO_n^+$.

Explore related subjects

math.QA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Daniel Gromada. 2022-08-11. Presentations of projective quantum groups. https://doi.org/10.5802/crmath.353

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism

An involutive Lie bialgebra induces a Batalin-Vilkovisky operator on its exterior algebra. We introduce a graded generalization of the necklace Lie bialgebra, which depends on a choice of a quiver $Q$. We relate the resulting Batalin-Vilkovisky structure to the Batalin-Vilkovisky structure coming from a degree $-1$ symplectic form on a suitably defined representation variety of the quiver $Q$. The morphism intertwining these Batalin-Vilkovisky algebras will be given by a twisted trace, recovering the usual (super)trace and the odd trace.

math.QA↗
arXiv2026

Freeness and divisibility for right $H$-simple left $H$-comodule algebras over a pointed Hopf algebra $H$

Let $H$ be a pointed Hopf algebra and let $A$ be a right $H$-simple left $H$-comodule algebra. We show that every relative $(H,A)$-Hopf module is free as an $A$-module and that this freeness characterizes the class of pointed Hopf algebras. We give a criterion for the category of relative $(H,A)$-Hopf modules to be semisimple. We also show that $A$ can be embedded into a left $H$-comodule algebra of a specific form when $H$ and $A$ are $\mathbb{N}_0$-graded. As a consequence, we prove that if $H$ is finite-dimensional and $A^{\mathrm{co} H}=\Bbbk$, then $A$ is finite-dimensional and $\dim A$ divides $\dim H$.

math.QA↗
arXiv2026

$C_2$-Cofiniteness and Rationality of the Icosahedral Orbifold $V_{L_2}^{A_5}$

Let $L_2=\mathbb{Z}α$ be the rank-one root lattice with $(α,α)=2$, and let $A_5$ act on the lattice vertex operator algebra $V_{L_2}$ through an icosahedral subgroup of $\operatorname{Aut}(V_{L_2})\cong PSL_2(\mathbb{C})$. We prove that the fixed-point vertex operator algebra $V_{L_2}^{A_5}$ is strongly rational.

math.QA↗