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Introduction Examples of regular leave algebras n

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44 pages
Introduction Examples of regular leave algebras, n = 3 Heisenberg invariancy, Poisson structures on Moduli spaces, Odesskii-Feigin-Polishchuk Cremona transformations and Poisson morphisms of P4 Polynomial and Elliptic Algebras of small dimensions. Vladimir Roubtsov1 1LAREMA, U.M.R. 6093 associé au CNRS Université d'Angers and Theory Division, ITEP, Moscow Novembre, 27, 2009 - Claude Roger -2009, Lyon Vladimir Roubtsov Claude Roger 2009, Congrès International, novembre, Lyon

  • lie algebra

  • poisson

  • leave algebras

  • algebras associated

  • odesskii-feigin-polishchuk cremona

  • dx2 ?


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Introduction Examples of regular leave algebras,n=3 Heisenberginvariancy,PoissonstructuresonrMphoidsumlissopfacPe4s, Cremona transformations and Poisson mo
"Polynomial
and Elliptic Algebras dimensions."
Vladimir
Roubtsov1
of
"small
1LAREMA, U.M.R. 6093 associé au CNRS Université d’Angers and Theory Division, ITEP, Moscow
Novembre,
27, 2009 - "Claude Roger -2009", Lyon
Vladimir Roubtsov
"Claude Roger 2009", Congrès International, novembre, Lyon
Introduction Examples of regular leave algebras,n=3 Heisenberg invariancy, Poisson structures on Moduli spacPe4s, Cremona transformations and Poisson morphisms of
To
60-th
anniversary
of
Vladimir Roubtsov
my
friend
Claude
Roger
"Claude Roger 2009", Congrès International,
novembre, Lyon
Introduction Examples of regular leave algebras,n=3 Heise i s a Crenmboenragitnrvaanrsifaonrcmy,atPiooinsssoannsdtrPuocitsusroensomnorMpohidsumlspofcPe4s, Plan
1
2
3
4
Introduction Poisson algebras associated to elliptic curves.
Examples of regular leave algebras,n=3 Elliptic algebras "Mirror transformation"
Heisenberg invariancy, Poisson structures on Moduli spaces, Odesskii-Feigin-Polishchuk
Cremona transformations and Poisson morphisms ofP4
Vladimir Roubtsov
"Claude Roger 2009", Congrès International, novembre, Lyon
Introduction Examples of regular leave algebras,n=3 Heisenberngaitnrvaanrsifaonrcmy,atPiooinsssoannsdtrPuocitsusroensomnorMpohidsumlisspofacPe4s, Cremo
Polynomial Poisson structures Poisson algebras associated to elliptic curves.
APoisson structureon a manifoldM(smooth or algebraic) is given by a bivector antisymmetric tensor fieldπΛ2(TM)defining on the corresponded algebra of functions onMa structure of (infinite dimensional) Lie algebra by means of thePoisson brackets
{f,g}=hπ,dfdgi.
The Jacobi identity for this brackets is equivalent to an analogue of (classical) Yang-Baxter equation namely to the "Poisson Master Equation":[π, π] =0, where the brackets [,] : Λp(TM)×Λq(TM)7→Λp+q1(TM)are the only Lie super-algebra structure onΛ.(TM).
Vladimir Roubtsov
"Claude Roger 2009", Congrès International, novembre, Lyon