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2016•Linear and Multilinear AlgebraRequires access

Extension of algebras and its applications to the real Clifford algebras

Doohann Lee, Youngkwon Song

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Abstract

Extension of algebras can be constructed through various manners. In this paper, we introduce a new way of construction to extend a given algebra of dimension , which is isomorphic to the real Clifford algebra , to another algebra of dimension over the real numbers. And then, we generalize the construction over a -grading algebra. Moreover, we will show the relation between the new constructed algebras and Clifford algebras.

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What this paper is about

Extension of algebras can be constructed through various manners. In this paper, we introduce a new way of construction to extend a given algebra of dimension , which is isomorphic to the real Clifford algebra , to another algebra of dimension over the real numbers. And then, we generalize the construction over a -grading algebra. Moreover, we will show the relation between the new constructed algebras and Clifford algebras.

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Available abstract

Extension of algebras can be constructed through various manners. In this paper, we introduce a new way of construction to extend a given algebra of dimension , which is isomorphic to the real Clifford algebra , to another algebra of dimension over the real numbers. And then, we generalize the construction over a -grading algebra. Moreover, we will show the relation between the new constructed algebras and Clifford algebras.

Key concepts: Clifford algebra, Mathematics, Classification of Clifford algebras, Extension (predicate logic), Geometric algebra, Algebra over a field, Jordan algebra, Dimension (graph theory)

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