discrete minimal surface algebras

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ID: 143993
2010
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Abstract
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl_n (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
Reference Key
arnlind2010symmetry,discrete Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Joakim Arnlind;Jens Hoppe
Journal Therapeutic drug monitoring
Year 2010
DOI
DOI not found
URL
http://dx.doi.org/10.3842/SIGMA.2010.042
Keywords
yang-mills algebramathematics

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