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cyclic derivation
Given a field , a cyclic derivation on an -algebra (example: algebra of formal noncommutative power series in -variables) is an -linear map satisfying
Given a cyclic derivation a corresponding cyclic derivative is defined by .
They are appearing in the definition of Jacobian algebra(also called Jacobi algebra) of a quiver with potential, see there.
- Gian-Carlo Rota, Bruce Sagan, Paul R.Stein, A cyclic derivative in noncommutative algebra, J. Algebra 64:1 (1980) 54-75 doi MR575782
- Christophe Reutenauer, Cyclic derivation of noncommutative algebraic power series, J. Alg. 85, 32-39 (1983)
- Daniel Lopez-Aguayo, Cyclic derivations, species realizations and potentials, pdf
A class of identities involving multiple zeta functions is described using cyclic derivations in
- Michael E.Hoffman, Yasuo Ohno, Relations of multiple zeta values and their algebraic expression, J. Algebra 262:2 (2003) 332-347 doi
Last revised on September 14, 2022 at 13:44:04.
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