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|Title: ||Bicrossproducts of algebraic quantum groups|
|Authors: ||Delvaux, L.|
Van Daele, A.
|Issue Date: ||2013|
|Citation: ||International journal of mathematics, 24 (1), p. 1-48|
|Abstract: ||Let A and B be two algebraic quantum groups. Assume that B is a right A-module algebra
and that A is a left B-comodule coalgebra. If the action and coaction are matched,
it is possible to define a coproduct Δ# on the smash product A#B making the pair
(A#B,Δ#) into an algebraic quantum group.
In this paper we study the various data of the bicrossproduct A#B, such as the
modular automorphisms, the modular elements, . . . and we obtain formulas in terms of
the data of the components A and B. Secondly, we look at the dual of A#B (in the sense
of algebraic quantum groups) and we show it is itself a bicrossproduct (of the second
type) of the duals b A and bB.
We give some examples that are typical for algebraic quantum groups. In particular,
we focus on the extra structure, provided by the integrals and associated objects. It
should be mentioned that with examples of bicrossproducts of algebraic quantum groups,
we do get examples that are essentially different from those commonly known in Hopf
|ISI #: ||000316806500004|
|Type: ||Journal Contribution|
|Validation: ||ecoom, 2014|
|Appears in Collections: ||Research publications|
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