## 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.

**Download:** **PDF**

### Submission history

[v1] 24 Sep 2009

**Unique-IP document downloads:** 150 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*