<%@LANGUAGE="VBSCRIPT" CODEPAGE="CP_ACP"%> Bracket Algebra and Its Generalizations

Hongbo Li

Abstract: Bracket algebra is a classical tool in algebraic invariant theory. In the 1970s, the Rota school rejuvinated this algebraic language for the purpose of symbolic computation in synthetic projective geometry. In the 1980s, they further generalized bracket algebra to superalgebra to unify and extend the classical symmetric and antisymmetric algebras. In recent years, I extend bracket algebra from projective geometric framework to Euclidean one, and establish a powerful algebraic tool for Euclidean geometric symbolic computation -- Clifford bracket algebra. In this talk, I shall survey the history and development of bracket algebra and its generalizations up to recent years.