## Algebra   ## Construction of Multivector Inverse for Clif Ford Algebras Over 2m+1-Dimensional Vector Spaces from Multivector Inverse for Clifford Algebras Over 2m-Dimensional Vector Spaces

Authors: Eckhard Hitzer, Stephen J. Sangwine

Assuming known algebraic expressions for multivector inverses in any Clifford algebra over an even dimensional vector space R^{p',q'), n' = p' +q' = 2m, we derive a closed algebraic expression for the multivector inverse over vector spaces one dimension higher, namely over R^{p,q}, n = p+q = p'+q'+1 = 2m+1. Explicit examples are provided for dimensions n' = 2,4,6, and the resulting inverses for n = n' +1 = 3,5,7. The general result for n = 7 appears to be the first ever reported closed algebraic expression for a multivector inverse in Clifford algebras Cl(p,q), n = p + q = 7, only involving a single addition of multivector products in forming the determinant.

Comments: Advances of Applied Clifford Algebras, Vol. 29, article #29, 22 pages, First Online: 19 February 2019. DOI: 10.1007/s00006-019-0942-7.