Abstract
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 ∂: A → A. We obtain several results concerning the kernel of ∂; for instance this kernel is a subalgebra of A that is free of rank d.
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