TY - JOUR
T1 - Algebraic classical W-algebras and Frobenius manifolds
AU - Dinar, Yassir Ibrahim
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2021/10
Y1 - 2021/10
N2 - We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.
AB - We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.
KW - Classical W-algebra
KW - Common equilibrium points
KW - Drinfeld–Sokolov reduction
KW - Exact Poisson pencil
KW - Frobenius manifolds
KW - Nilpotent orbits in Lie algebras
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U2 - 10.1007/s11005-021-01458-2
DO - 10.1007/s11005-021-01458-2
M3 - Article
AN - SCOPUS:85114352935
SN - 0377-9017
VL - 111
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 5
M1 - 115
ER -