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Character algebras of
decorated $\operatorname{SL}_2(C)$–local systems
Greg Muller and Peter Samuelson |
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Algebraic & Geometric Topology 13 (2013) 2429–2469
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Abstract |
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Let be a connected and locally 1–connected space, and let . A decorated –local system is an –local system on , together with a chosen element of the stalk at each component of . We study the decorated –character algebra of : the algebra of polynomial invariants of decorated –local systems on . The character algebra is presented explicitly. The character algebra is shown to correspond to the –algebra spanned by collections of oriented curves in modulo local topological rules. As an intermediate step, we obtain an invariant-theory result of independent interest: a presentation of the algebra of –invariant functions on , where is the tautological representation of . |
Keywords
local systems, rings of invariants, mixed invariants, mixed
concomitants, skein algebra, cluster algebra, quantum
cluster algebra, quantum torus, triangulation of surfaces
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Mathematical Subject Classification 2010
Primary: 13A50, 14D20, 57M27, 57M07
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References |
Publication
Received: 10 November 2011
Revised: 24 February 2013
Accepted: 11 March 2013
Published: 4 July 2013
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Authors |
| Greg Muller | |
| Mathematics Department Louisiana State University 7250 Perkins Rd Apt 217 Baton Rouge, LA 70808 USA |
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| https://www.math.lsu.edu/~gmuller/ | |
| Peter Samuelson | |
| Department of Mathematics University of Toronto Bahen Centre 40 George St. Rm 6290 Toronto, ON M5S 2E4 Canada |
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| http://www.math.toronto.edu/cms/samuelson-peter/ | |
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