On the Nature of the Virasoro Algebra
نویسنده
چکیده
The multiplication in a quasiassociative algebra R satisfies the property a ∗ (b ∗ c)− (a ∗ b) ∗ c = b ∗ (a ∗ c)− (b ∗ a) ∗ c, a, b, c ∈ R. (∗∗) This property is necessary and sufficient for the Lie algebra Lie(R) to have a phase space. The above formulae are put into a cohomological framework, with the relevant complex being different from the Hochschild one even when the relevant quasiassociative algebra R becomes associative. Formula (∗) above also has a differentialvariational counterpart.
منابع مشابه
Lie triple derivation algebra of Virasoro-like algebra
Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.
متن کاملNoether current from the surface term of gravitational action, Virasoro algebra, and horizon entropy
We describe a simple way of obtaining horizon entropy using the approach based on the Virasoro algebra and central charge. We show that the Virasoro algebra defined by the Noether currents corresponding to the surface term of gravitational action, for the diffeomorphisms which leave the horizon structure unaltered, has a central extension that directly leads to the horizon entropy. In this appr...
متن کاملBi-Hamiltonian nature of the equation u_tx=u_xyu_y-u_yyu_x
We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in [16]) is a generalization of the classical Virasoro algebra to the case of two space variables. Two main examples of integrable equations we obtain are quite well known. We show t...
متن کاملDiscrete Lagrangian Systems on the Virasoro Group and Camassa-holm Family
We show that the continuous limit of a wide natural class of the right-invariant discrete Lagrangian systems on the Virasoro group gives the family of integrable PDE’s containing Camassa-Holm, Hunter-Saxton and Korteweg-de Vries equations. This family has been recently derived by Khesin and Misio-lek as Euler equations on the Virasoro algebra for H1 α,βmetrics. Our result demonstrates a univers...
متن کاملOn the quantum super Virasoro algebra
The quantum super-algebra structure on the deformed super Virasoro algebra is investigated. More specifically we established the possibility of defining a non trivial Hopf super-algebra on both one and two-parameters deformed super Virasoro algebras. ∗e-mail: [email protected]
متن کاملDiscrete-Time Quantum Field Theory and the Deformed Super Virasoro Algebra
The deformed Virasoro algebra plays a similar role for deformed conformal fields as the Virasoro algebra in the usual string and conformal field theories. We show that there exists a physical theory, the discrete-time QFT, in which framework the deformations of (super)Virasoro algebra constructed earlier on an abstract mathematical background emerge. Specifically, the deformed Virasoro and supe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998