Supports and Groups in Meson Algebras

Abstract

Meson algebras B(M, ϕ) are presumed to intervene in Physics in the same way as Clifford algebras; this motivates a study of meson algebras based on cliffordian ideas. The concept of support in M of an element of B(M, ϕ) is investigated: this support proves to be the sum of two partial supports. Then Clifford groups and Lipschitz groups are studied in relation to an orthogonal group and with somewhat weak hypotheses: M is any vector space over any field K, and ϕ any symmetric bilinear form M × M → K. Mathematics Subject Classification (2010). 11E88, 15A78, 16S10, 15A63.