# An F5 Algorithm for Modules Over Path Algebra Quotients and the Computation of Loewy Layers

Tuesday, June 2, 2015 - 2:30pm - 3:30pm

Lind 305

Simon King (Friedrich-Schiller-Universität)

The F5 algorithm is a signature based algorithm to compute Gröbner bases for modules over polynomial rings. The F5 signature allows to exploit commutativity relations in order to avoid redundant computations. When considering modules over path algebra quotients, one can instead exploit the quotient relations to avoid redundancies.

For my applications, it is important that Gröbner bases are actually not more than a by-product of the F5 algorithm. Indeed, the F5 signature provides additional information: If the quotient algebra is a basic algebra and if a negative degree monomial ordering is used, then the F5 signature allows to read off the Loewy layers of the module. It is currently attempted to provide an efficient implementation of the algorithm in SageMath.

For my applications, it is important that Gröbner bases are actually not more than a by-product of the F5 algorithm. Indeed, the F5 signature provides additional information: If the quotient algebra is a basic algebra and if a negative degree monomial ordering is used, then the F5 signature allows to read off the Loewy layers of the module. It is currently attempted to provide an efficient implementation of the algorithm in SageMath.

MSC Code:

65-XX

Keywords: