A Clifford algebra realization of Supersymmetry and its Polyvector extension in Clifford Spaces Carlos Castro Center for Theoretical Studies of Physical Systems Clark Atlanta University, Atlanta, GA. 30314; perelmanc@hotmail.com June 2010 Abstract It is shown explicitly how to construct a novel (to our knowledge) realization of the Poincare superalgebra in 2D. These results can be ex- tended to other dimensions and to (extended) superconformal and (anti) de Sitter superalgebras. There is a fundamental difference between the findings of this work with the other approaches to Supersymmetry (over the past four decades) using Grassmannian calculus and which is based on anti-commuting numbers. We provide an algebraic realization of the anti- commutators and commutators of the 2D super-Poincare algebra in terms of the generators of the tensor product Cl1,1(R) ⊗A of a two-dim Clifford algebra and an internal algebra A whose generators can be represented in terms of powers of a 3 × 3 matrix Q, such that Q 3 = 0. Our real- ization differs from the standard realization of superalgebras in terms of dif f erential operators in Superspace involving Grassmannian (anti- commuting) coordinates θ α and bosonic coordinates x μ . We conclude in the final section with an analysis of how to construct Polyvector-valued ex- tensions of supersymmetry in Clifford Spaces involving spinor-tensorial su- percharge generators Q μ 1 μ 2 .....μn α and momentum polyvectors Pμ 1 μ 2 ....μn . Clifford-Superspace is an extension of Clifford-space and whose symmetry transformations are generalized polyvector-valued supersymmetries. KEYWORDS : Clifford algebras; Supersymmetry; Polyvector-supersymmetry; M, F theory superalgebras. 1 Clifford algebra realization of Supersymmetry Clifford algebras have been a very useful tool for a description of geometry and physics [4], [5]. In [5],[3],[6] it was proposed that every physical quantity is in fact 1