Defining relations for the exceptional Lie superalgebras of vector fields pertaining to The Standard Model

Details Defining relations for the exceptional Lie superalgebras of vector fields pertaining to The Standard Model Defining relations for the exceptional Lie superalgebras of vector fields pertaining to The Standard Model

2002-02-18

arxiv.org/abs/math-ph/0202025v1

In: C.Duval, L.Guieu, V.Ovsienko (eds.) The orbit method in geometry and physics: in honor of A.A.Kirillov. Progress in Mathem

Physics

Mathematical Physics

42 pages, Latex

Scientific paper

We list defining relations for the four of the five exceptional simple Lie superalgebras some of which, as David Broadhurst conjectured and Kac demonstrated, may pertain to The Standard Model or Grand unified theories of elementary particles. For the fifth superalgebra the result is not final: there might be infinitely many relations. Contrariwise, for the same Lie superalgebra with Laurent polynomials as coefficients there are only finitely many relations.

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