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Algebra, Geometry and Mathematical Physics pp 83–97Cite as

Subalgebra Depths Within the Path Algebra of an Acyclic Quiver

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 85))

Abstract

Constraints are given on the depth of diagonal subalgebras in generalized triangular matrix algebras. The depth of the top subalgebra \(B \cong A / \mathrm{rad}\,A\) in a finite, connected, acyclic quiver algebra \(A\) over an algebraically closed field \(\mathbb {K}\,\) is then computed. Also the depth of the primary arrow subalgebra \(1\mathbb {K}\,+ \mathrm{rad}\,A = B\) 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.

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Acknowledgments

The authors would like to thank Sebastian Burciu for visiting Porto in May 2012 and discussing topics related to this paper. Research on this paper was partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT under the project PE-C/MAT/UI0144/2011.

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Authors and Affiliations

  1. Departamento de Matematica, Faculdade de Ciencias da Universidade do Porto, 687 Rua Campo Alegre, 4169-007 , Porto, Portugal

    Lars Kadison & Christopher J. Young

Authors
  1. Lars Kadison
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  2. Christopher J. Young
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Corresponding author

Correspondence to Lars Kadison .

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Editors and Affiliations

  1. Informatique et Applications, Université of Haute Alsace, Laboratoire de Mathématiques, Mulhouse, France

    Abdenacer Makhlouf

  2. Tallinn University of Technology, Dept. Mathematics, Tallinn, Estonia

    Eugen Paal

  3. Culture and Communication (UKK) Division of Applied Mathematics, Mälardalen University, The School of Education, Västerås, Sweden

    Sergei D. Silvestrov

  4. Dept. Mathematical Sciences, University of Göteborg, Göteborg, Sweden

    Alexander Stolin

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Kadison, L., Young, C.J. (2014). Subalgebra Depths Within the Path Algebra of an Acyclic Quiver. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds) Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55361-5_6

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