Representations for the Nongraded Virasoro-Like Algebra
نویسندگان
چکیده
منابع مشابه
Representations for the Non-graded Virasoro-like Algebra
It is proved in this paper that an irreducible module over the non-graded Virasoro-like algebra L, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, we give the complete classification of indecomposable L-modules V = ⊕ m,n∈Z Cvm,n which satisfy Lr,svm,n ⊆ Cvr+m,s+n+1 + Cvr+m,s+n.
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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.
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Some representations π of b of particular interest [2] are the Verma modules (V, π) = (V , π), h, c ǫ R. They are characterized by the following conditions. (i) There is a vector v = vφ 6= 0 in V such that Lnv = 0, n > 0, L0v = hv, Zv = cv. (ii) Let A be the set of sequences of integers k1,≥ k2 ≥ . . . ≥ kr > 0 of arbitrary length, and if α ǫ A let vα = π(L−k1) . . . π(L−kr)vφ. Then {vα|α ǫ A} ...
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We consider representations of the Virasoro algebra, a one-dimensional central extension of the Lie algebra of vectorfields on the unit circle. Positive-energy, highest weight and Verma representations are defined and investigated. The Shapovalov form is introduced, and we study Kac formula for its determinant and some consequences for unitarity and degeneracy of irreducible highest weight repr...
متن کاملOn unitary representations of the Virasoro algebra*
Some representations π of b of particular interest [2] are the Verma modules (V, π) = (V , π), h, c R. They are characterized by the following conditions. (i) There is a vector v = vφ = 0 in V such that Lnv = 0, n > 0, L0v = hv,Zv = cv. (ii) Let A be the set of sequences of integers k1,≥ k2 ≥ . . . ≥ kr > 0 of arbitrary length, and if α A let vα = π(L−k1) . . . π(L−kr)vφ. Then {vα|α A} is a bas...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2010
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927871003603796