General twisting of algebras

Details General twisting of algebras General twisting of algebras

2006-05-03

arxiv.org/abs/math/0605086v2

Advances in Mathematics, 212 (1), 315-337 (2007)

Mathematics

Quantum Algebra

19 pages

Scientific paper

10.1016/j.aim.2006.10.003

We introduce the concept of pseudotwistor (with particular cases called twistor and braided twistor) for an algebra $(A, \mu, u)$ in a monoidal category, as a morphism $T:A\otimes A\to A\otimes A$ satisfying a list of axioms ensuring that $(A, \mu \circ T, u)$ is also an algebra in the category. This concept provides a unifying framework for various deformed (or twisted) algebras from the literature, such as twisted tensor products of algebras, twisted bialgebras and algebras endowed with Fedosov products. Pseudotwistors appear also in other topics from the literature, e.g. Durdevich's braided quantum groups and ribbon algebras. We also focus on the effect of twistors on the universal first order differential calculus, as well as on lifting twistors to braided twistors on the algebra of universal differential forms.

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