FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 2, PAGES 549-577

Differential calculi on standard quantizations of simple algebraic groups

M. F. Sadykov

Abstract

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In the present paper differential calculi on quantum groups are studied, following S. L. Woronowisz. A non-existence of bicovariant differential calculi on the standard quantizations of simple algebraic groups is proved, ground field is taken to be $$K=k(q). Left-covariant differential calculus on $SL$_q(2) is constructed and homology of algebra $U$_q(sl(2)) with coefficients in finite-dimensional modules is computed.

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