2 4 N ov 2 00 7 Rational R - matrices , centralizer algebras and tensor identities for e 6 and e 7 exceptional families of Lie algebras
نویسنده
چکیده
We use Cvitanović’s diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the e6 and e7 families of Lie algebras, and thus explain Westbury’s observations about their uniform spectral decompositions. In doing so we explore the extensions of the Brauer and symmetric group algebras to the centralizer algebras of e7 and e6 on their lowest-dimensional representations and (up to three-fold) tensor products thereof, giving bases for them and a range of identities satisfied by the algebras’ defining invariant tensors. [email protected] [email protected]
منابع مشابه
Rational R - matrices , centralizer algebras and tensor identities for e 6 and e 7 exceptional families of Lie algebras
We use Cvitanović’s diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the e6 and e7 families of Lie algebras, and thus explain Westbury’s observations about their uniform spectral decompositions. In doing so we explore the extensions of the Brauer and symmetric group algebras to the centralizer algebras of e7 and e6 on their lowest-dimension...
متن کاملRational R - matrices , centralizer algebras and tensor identities for e 6 and e 7 families of Lie algebras
We use Cvitanović’s diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the e6 and e7 families of Lie algebras, and thus explain Westbury’s observations about their uniform spectral decompositions. In doing so we explore the extensions of the Brauer and symmetric group algebras to the centralizer algebras of e7 and e6 on their lowest-dimension...
متن کاملar X iv : m at h / 06 11 83 1 v 1 [ m at h . R A ] 2 7 N ov 2 00 6 CLASSIFICATION OF 4 - DIMENSIONAL NILPOTENT COMPLEX
The Leibniz algebras appeared as a generalization of the Lie algebras. In this work we deal with the classification of nilpotent complex Leibniz algebras of low dimensions. Namely, the classification of nilpotent complex Leibniz algebras dimensions less than 3 is extended to the dimension four.
متن کاملar X iv : h ep - t h / 03 11 24 7 v 1 2 6 N ov 2 00 3 On representations of the exceptional superconformal algebra
A superconformal algebra is a simple complex Lie superalgebra g spanned by the coefficients of a finite family of pairwise local fields a(z) = ∑ n∈Z a(n)z , one of which is the Virasoro field L(z), [3, 8, 11]. Superconformal algebras play an important role in the string theory and conformal field theory. The Lie superalgebras K(N) of contact vector fields with Laurent polynomials as coefficient...
متن کاملNon-additive Lie centralizer of infinite strictly upper triangular matrices
Let $mathcal{F}$ be an field of zero characteristic and $N_{infty}(mathcal{F})$ be the algebra of infinite strictly upper triangular matrices with entries in $mathcal{F}$, and $f:N_{infty}(mathcal{F})rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $N_{infty }(mathcal{F})$; that is, a map satisfying that $f([X,Y])=[f(X),Y]$ for all $X,Yin N_{infty}(mathcal{F})...
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 2007