Yang–Baxter operators and noncommutative de Rham complexes

E. E. Mukhin


Abstract: Axiomatic approaches to the construction of differential calculi on quantum objects are studied in this paper. The connection between universal coacting semigroups and $R$-matrix quantum semigroups is investigated. Covariant quantum (noncommutative) de Rham complexes on quantum spaces, strong $R$-matrix quantum semigroups, and the quantum group $SL_q(2)$ are described.

UDC: 513.015

MSC: Primary 17B37, 16W25, 16W30; Secondary 58A10, 58H99, 81R50

Received: 13.10.1992

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:2, 315–338

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