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Braided modules and reflection equations

100%

Gurevich D.

Banach Center Publications

1997

tom 40

nr 1

99-110

We introduce a representation theory of q-Lie algebras defined earlier in [DG1], [DG2], formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in particular, those based on the so-called reflection equations. We also investigate the truncated tensor product of braided modules.

Quantization of pencils with a gl-type Poisson center and braided geometry

63%

Gurevich D., Saponov P.

Banach Center Publications

2011

tom 93

nr 1

145-162

We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and describe the corresponding quantum algebras. A few detailed examples are exhibited.

Ograniczanie wyników

2 Banach Center Publications

2 Gurevich D.

1 Saponov P.

1 2011

1 1997

Wyniki wyszukiwania

Braided modules and reflection equations

Quantization of pencils with a gl-type Poisson center and braided geometry