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First order optimum calculi. (English) Zbl 0883.16024
Summary: A new notion of optimum first order calculi was introduced by A. Borowiec, V. K. Kharchenko and Z. Oziewicz [Non-associative algebra and its applications, 3rd int. Conf. 1993, Math. Appl. Dordr. 303, 46-53 (1994; Zbl 0833.58006)]. A module of vector fields for a coordinate differential is defined. Some examples of optimal algebras for homogeneous bimodule commutations are presented. Classification theorem for homogeneous calculi with commutative optimal algebras in two variables is proved.

16W25 Derivations, actions of Lie algebras
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16D20 Bimodules in associative algebras
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
17B66 Lie algebras of vector fields and related (super) algebras