On Symmetry Properties of Frobenius Manifolds and Related Lie-Algebraic Structures [PDF]
Symmetry, 2021 The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. Our approach was based on a modification of the Adler–Kostant–Symes integrability scheme and applied to the co-adjoint orbits of the diffeomorphism loop group of the circle.
Anatolij K. Prykarpatski +1 more
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Frobenius structures and characters of affine Lie algebras [PDF]
, 2017 35 pages. In this revision, Proposition 5.4 in the previous version is divided into 4 Propositions (from Proposition 5.4 to Proposition 5.7).
Ikuo Satake
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Hopf Galois extensions, triangular structures, and Frobenius Lie algebras in prime characteristic [PDF]
Journal of Algebra, 2004 29 pages, plain ...
Serge Skryabin
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Classification of Frobenius, two-step solvable Lie poset algebras [PDF]
, 2020 We show that the isomorphism class of a two-step solvable Lie poset subalgebra of a semisimple Lie algebra is determined by its dimension. We further establish that all such algebras are absolutely rigid.
Coll, Vincent +2 more
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Computing invariants and semi-invariants by means of Frobenius Lie algebras [PDF]
Journal of Algebra, 2009 Let U(L) be the enveloping algebra of a finite dimensional Lie algebra L over a field k of characteristic zero, Z(U(L)) its center and Sz(U(L)) its semicenter. A sufficient condition is given in order for Sz(U(L)) to be a polynomial algebra over k. Surprisingly, this condition holds for many Lie algebras, especially among those for which the radical is
Alfons I. Ooms
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Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields [PDF]
, 1997 We construct a generalization of the variations of Hodge structures on Calabi-Yau manifolds.
Barannikov, Sergey, Kontsevich, Maxim
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QUASI FROBENIUS LIE ALGEBRAS CONSTRUCTION OF N=4 SUPERCONFORMAL FIELD THEORIES [PDF]
Modern Physics Letters A, 1996 The Manin triples construction of N =4 superconformal field theories is considered. A correspondence between quasi Frobenius finite-dimensional Lie algebras and N =4 Virasoro superalgebras is established.
S. E. Parkhomenko
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On extensions of Frobenius-Kahler and Sasakian Lie algebras [PDF]
Journal of Algebra and Its ApplicationsExtensions of Lie algebras equipped with Sasakian or Frobenius-Käahler geometric structures are studied. Conditions are given so that a double extension of a Sasakian Lie algebra be Sasakian again. Conditions are also given for obtaining either a Sasakian or a Frobenius-Käahler Lie algebra upon respectively extending a Frobenius-Käahler or a Sasakian ...
M. C. Rodriguez-Vallarte +2 more
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On systems of commuting matrices, Frobenius Lie algebras and Gerstenhaber's Theorem [PDF]
, 2020 This new version V2, 37 pages in Latex, contains substantial deep changes compared to version 1 which was only 12 pages. In particular, the present version includes deep discussions on the classification of 2-step solvable Frobenius Lie algebras and maximal Abelian subalgebras of sl(n,K)
Diatta, Andre +2 more
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Lie invariant Frobenius lifts on linear algebraic groups [PDF]
, 2018 We show that if $G$ is a linear algebraic group over a number field and if $G$ is not a torus then for all but finitely many primes $p$ the $p$-adic completion of $G$ does not possess a Frobenius lift that is "Lie invariant mod $p$" (in the sense of \cite{alie1}). This is in contrast with the situation of elliptic curves studied in \cite{alie1}.
Alexandru Buium
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