Convolution over Lie and Jordan algebras

Authors

  • Mohamed El Bachraoui

DOI:

https://doi.org/10.11575/cdm.v1i1.61883

Abstract

Given a ternary relation C on a set U and an algebra A, we present a construction of a convolution algebra A(U, C) of U = (U, C) over A. This generalises bothmatrix algebras and algebras obtained from convolution of monoids. To any class of algebras corresponds a class of convolution structures. Our study cases are the classes of commutative, associative, Lie, and Jordan algebras. In each of these classes we give conditions on (U, C) under which A(U, C) is in the same class as A. It turns out that in some situations these conditions are even necessary.

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Published

2006-03-24

Issue

Section

Articles