Clifford Algebras: What is the def. of "an Algebra generated froman inner-
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From: bacle on 11 Aug 2010 08:10 n the entry: http://en.wikipedia.org/wiki/Clifford_algebra the Clifford algebra is defined as the algebra freely generated by an inner-product space; in this case ,the Clifford n-algebra it is the algebra freely-generated by R^n with its standard inner product: I understand how, e.g., a set S freely-generates a vector space over R ( functions of finite- support, etc.). But I don't see how an inner-product space generates an algebra; clearly, the underlying vector space is passed-on from the inner-prod. space to the algebra, but the rest does not seem clear. I assume the inner-product, subject to some relations, is used to define multiplication, but I don't see clearly how this is done/defined.. Could anyone expliain or refer me to a source describing this process of an inner-product space generating an algebra more formally.? Thanks. |