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Algebraic approach to calculuses with partial derivatives. (English) Zbl 0852.16027
Summary: A calculus with partial derivatives for a unitary associative algebra is defined as a differential acting from the algebra to a right free bimodule. The notion of optimal algebra is extended to such calculuses. The canonical construction of a quantum de Rham complex is proposed for a calculus with partial derivatives.

MSC:
16W25 Derivations, actions of Lie algebras
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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