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Quantum Hilbert's fifth problem

Hilbert's fifth problem inquires whether every locally Euclidean group is necessarily a Lie group. Von Neumann demonstrated that this is indeed true for the compact case. The definition of a quantum ...
Sebastien Palcoux's user avatar
5 votes
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281 views

Is the "Toeplitz algebra" the representation ring of a Hopf algebra related to SU(2)?

More precisely, does there exist a Hopf algebra $H$ whose category of (finite-dimensional, complex) representations is generated under direct sum and tensor product by two one-dimensional ...
Qiaochu Yuan's user avatar
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Do the following two notions of quantum groups sometimes coincide?

On the one hand there is the notion of quantum groups due to Drinfeld and Jimbo. In there notion a quantum group is defined as a deformation of the universal enveloping algebra of a semisimple Lie ...
Raoul's user avatar
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Action of Hopf algebra of identity supported distributions on a Lie group

The Hopf algebra of identity supported distributions on a lie group is cocommutative. It is well known that it is a group object in the category of cocommutative coalgebras. Is there a canonical ...
Lefevres's user avatar
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Concrete examples of quantum duality principle

Let $G$ be a Poisson Lie group, $\mathfrak{g}$ be a Lie algebra of $G$, $G^*$ be a dual of $G$, $\mathscr{C}(G^*)$ be a Poisson algebra of $G^*$, and $U_h(\mathfrak{g})$ be a quantized universal ...
yohei ohta's user avatar