Noetherianity of some degree two twisted skew-commutative algebras
| Autor: | Rohit Nagpal, Steven V Sam, Andrew Snowden |
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| Rok vydání: | 2016 |
| Předmět: |
Physics::Physics and Society
Pure mathematics General Mathematics Open problem 13E05 General Physics and Astronomy Lie superalgebra 0102 computer and information sciences Commutative Algebra (math.AC) math.RT 01 natural sciences Representation theory Wedge (geometry) Mathematics::Algebraic Topology FOS: Mathematics 0101 mathematics Representation Theory (math.RT) Commutative property Mathematics 010102 general mathematics Skew 13A50 Mathematics - Commutative Algebra math.AC Pure Mathematics Cohomology 010201 computation theory & mathematics Bounded function Mathematics - Representation Theory 13E05 13A50 |
| Zdroj: | Selecta Mathematica, vol 25, iss 1 Nagpal, Rohit; Sam, Steven V; & Snowden, Andrew. (2019). Noetherianity of some degree two twisted skew-commutative algebras. SELECTA MATHEMATICA-NEW SERIES, 25(1). doi: 10.1007/s00029-019-0461-3. UC San Diego: Retrieved from: http://www.escholarship.org/uc/item/5kf8c71t Selecta Mathematica, New Series, vol 25, iss 1 |
| DOI: | 10.48550/arxiv.1610.01078 |
| Popis: | A major open problem in the theory of twisted commutative algebras (tca's) is proving noetherianity of finitely generated tca's. For bounded tca's this is easy, in the unbounded case, noetherianity is only known for Sym(Sym^2(C^\infty)) and Sym(\wedge^2(C^\infty)). In this paper, we establish noetherianity for the skew-commutative versions of these two algebras, namely \wedge(Sym^2(C^\infty)) and \wedge(\wedge^2(C^\infty)). The result depends on work of Serganova on the representation theory of the infinite periplectic Lie superalgebra, and has found application in the work of Miller-Wilson on "secondary representation stability" in the cohomology of configuration spaces. Comment: 22 pages |
| Databáze: | OpenAIRE |
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