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Subalgebra depths within the path algebra of an acyclic quiver

Constraints are given on the depth of diagonal subalgebras in generalized triangular matrix algebras. The depth of the top subalgebra B = A /rad A in a finite, connected, acyclic quiver algebra A over an algebraically closed field K is then computed. Also the depth of the primary arrow subalgebra 1K + rad A = B in A is obtained. The two types of subalgebras have depths 3 and 4 respectively, independent of the number of vertices. An upper bound on depth is obtained for the quotient of a subalgebra pair.

preprint2013arXivOpen access
Lars KadisonChristopher J. Young
math.RT
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Lars KadisonChristopher J. Young

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