Lars Kadison, Christopher J. Young
Published 2013-02-07Version 1
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.
Comments: 14 pp. to appear in Proceedings A.G.M.P. Conf. Mulhouse, 2011, Springer
Biserial algebras via subalgebras and the path algebra of D_4
Path algebras of quivers and representations of locally finite Lie algebras
Rigid modules and ICE-closed subcategories over path algebras
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