Down-Up Algebras From Trees |
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Authors: | Ellen Kirkman |
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Institution: | Department of Mathematics , Wake Forest University , Winston-Salem , North Carolina , USA |
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Abstract: | It is shown that the global dimension of any n-ary down-up algebra A n = A(n,α, β,γ) is less than or equal to n + 2, and when γ i = 0 for all i (A n is graded by total degree in the generators), then the global dimension of A n is n + 2. Furthermore, a sufficient condition for A n to be prime is given; when γ i = 0 for all i this condition is also necessary. An example is given to show that the condition is not always necessary. |
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Keywords: | Down-up algebras Homological dimension Prime rings |
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