## On n-ary Algebras, Branes and Polyvector Gauge Theories in Noncommutative Clifford Spaces

**Authors:** Carlos Castro

Polyvector-valued gauge field theories in noncommutative Clifford spaces
are presented. The noncommutative star products are associative and
require the use of the Baker-Campbell-Hausdorff formula. Actions for pbranes
in noncommutative (Clifford) spaces and noncommutative phase
spaces are provided. An important relationship among the n-ary commutators
of noncommuting spacetime coordinates [X^{1},X^{2}, ......,X^{n}] with the
poly-vector valued coordinates X^{123...n} in noncommutative Clifford spaces
is explicitly derived [X^{1},X^{2}, ......,X^{n}] = n! X^{123...n}. The large N limit of
n-ary commutators of n hyper-matrices X_{i1i2}....in leads to Eguchi-Schild
p-brane actions for p + 1 = n. Noncommutative Clifford-space gravity as
a poly-vector-valued gauge theory of twisted diffeomorphisms in Clifford spaces
would require quantum Hopf algebraic deformations of Clifford
algebras.

**Comments:** 25 Pages. This article has been submitted to the J. Math. Phys.

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### Submission history

[v1] 24 Sep 2009

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