科研之友
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摘要
For a field F and an integer d >= 1, we consider the universal associative F-algebra A generated by two sets of d + 1 mutually orthogonal idempotents. We display four bases for the F-vector space A that we find attractive. We determine how these bases are related to each other. We describe how the multiplication in A looks with respect to our bases. Using our bases we obtain an infinite nested sequence of two-sided ideals for A. Using our bases we obtain an infinite exact sequence involving a certain F-linear map partial derivative: A -> A. We obtain several results concerning the kernel of partial derivative; for instance this kernel is a subalgebra of A that is free of rank d.
- 出版日期2010-12
