Donald Yau 2009 J. Phys. A: Math. Theor. 42 165202 doi:10.1088/1751-8113/42/16/165202
The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras
Donald Yau
Show affiliationsWe study a twisted version of the Yang–Baxter equation, called the Hom–Yang–Baxter equation (HYBE), which is motivated by Hom–Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom–Lie algebras and the others from Drinfeld's (dual) quasi-triangular bialgebras. Each solution of the HYBE can be extended to operators that satisfy the braid relations. Assuming an invertibility condition, these operators give a representation of the braid group.
- PACS
- MSC
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81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
- Subjects
- Dates
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Issue 16 (24 April 2009)
Received 10 January 2009, in final form 19 February 2009
Published 24 March 2009
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The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras
Donald Yau 2009 J. Phys. A: Math. Theor. 42 165202
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