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Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations
Abstract
Two groups G, H are said to be a matched pair if they act on each other and these actions, (a, /?), obey a certain compatibility condition.In such a situation one may form a bicrossproduct group, denoted Gβ cχi Q H. Also in this situation one may form a bicrossproduct Hopf, Hopf-von Neumann or Kac algebra obtained by simultaneous cross product and cross coproduct.We show that every compact semi-simple simply-connected Lie group G is a member of a matched pair, denoted (G, G*) 9 in a natural way.As an example we construct the matched pair in detail in the case (SU(2), SU( 2)*) where SU(2)* = is the simply-connected group of a Lie algebra su(2)*.Here su(2)* is defined with respect to a standard canonical solution of the CYBE on the complexification of su(2).
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Cited by
Bicrossproduct structure of κ-Poincare group and non-commutative geometry
Majid, S., & Ruegg, H. (1994) · Physics Letters B · doi:10.1016/0370-2693(94)90699-8 · Cited by 799
Self-citationQuantum groups and noncommutative geometry
Majid, S. (2000) · Journal of Mathematical Physics · doi:10.1063/1.533331 · Cited by 92
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Metadata
- Authors
- Majid, S.
- Venue
- Pacific Journal of Mathematics
- Publisher
- Mathematical Sciences Publishers
- Published
- 1990-02-01
- Volume
- 141
- Issue
- 2
- Pages
- 311-332
- ISSN
- 0030-8730 (ISSN-L)
- OpenAlex
- W2039011617
- Cited by
- 175
- References
- 0
- FWCI
- 16.21
- Type
- journal article
- Language
- en
- Open access
- closed
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- Majid, S. (1990). Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations. Pacific Journal of Mathematics. https://doi.org/10.2140/pjm.1990.141.311
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