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Book Sections Year : 2019

Noncommutative linear rewriting: applications and generalizations

Philippe Malbos

Abstract

These notes were intended for a lecture given at the Kobe summer school in July 2015. We present the notion of polygraphic presentation for algebras and their properties of confluence and termination, as introduced in [GHM17]. These presentations, called linear polygraphs, are rewriting systems that generalize noncommutative Gröbner bases, as studied by Bokut, [Bok76], Bergman, [Ber78], and Mora, [Mor94], in the sense that the orientation of the rewriting rules does not depend of a monomial order. We give a description of an algorithm given by Anick, [Ani86], for computing a free resolution of right modules over an algebra presented by a noncommutative Gröbner basis. Finally, we briefly sketch a method to compute polygraphic resolutions for an algebra presented by a confluent and terminating linear polygraph introduced in [GHM17].
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hal-01718880 , version 1 (27-02-2018)

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  • HAL Id : hal-01718880 , version 1

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Philippe Malbos. Noncommutative linear rewriting: applications and generalizations. Two algebraic byways from differential equations: Gröbner bases and quivers, 28, Springer, inPress, Algorithms and Computations in Mathematics. ⟨hal-01718880⟩
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