Poisson-Lie Odd Bracket on Grassmann Algebra
نویسندگان
چکیده
منابع مشابه
On an Isospectral Lie-Poisson System and Its Lie Algebra
In this paper we analyse the matrix differential system X ′ = [N,X], where N is skew-symmetric and X(0) is symmetric. We prove that it is isospectral and that it is endowed with a Poisson structure, and discuss its invariants and Casimirs. Formulation of the Poisson problem in a Lie–Poisson setting, as a flow on a dual of a Lie algebra, requires a computation of its faithful representation. Alt...
متن کاملLie - Poisson Deformation of the Poincaré Algebra
We find a one parameter family of quadratic Poisson structures on R 4 × SL(2, C) which satisfies the property a) that it is preserved under the Lie-Poisson action of the Lorentz group, as well as b) that it reduces to the standard Poincaré algebra for a particular limiting value of the parameter. (The Lie-Poisson transformations reduce to canonical ones in that limit, which we therefore refer t...
متن کاملLie Bialgebra Structures on Twodimensional Galilei Algebra and Their Lie–poisson Counterparts
All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie–Poisson structures on Galilei group are found. ∗Supported by the Lódź University Grant No.487
متن کاملLie-poisson Structure on Some Poisson Lie Groups
Poisson Lie groups appeared in the work of Drinfel'd (see, e.g., [Drl, Dr2]) as classical objects corresponding to quantum groups. Going in the other direction, we may say that a Poisson Lie group is a group of symmetries of a phase space that are allowed to "twist," in a certain sense, the symplectic or Poisson structure. The Poisson structure on the group controls this twisting in a precise w...
متن کاملA Poisson Bracket on Multisymplectic Phase Space ∗
A new Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined. At least for forms of degree n − 1, where n is the dimension of space-time, Jacobi's identity is fulfilled.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2006
ISSN: 1815-0659
DOI: 10.3842/sigma.2006.036