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283
Tilings of orthogonal polygons with similar rectangles or triangles
 Journal of Applied Mathematics & Computing
"... Abstract. In this paper we prove two results about tilings of orthogonal polygons. (1) Let P be an orthogonal polygon with rational vertex coordinates and let R(u) be a rectangle with side lengths u and 1. An orthogonal polygon P can be tiled with similar copies of R(u) if and only if u is algebra ..."
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Cited by 2 (0 self)
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Abstract. In this paper we prove two results about tilings of orthogonal polygons. (1) Let P be an orthogonal polygon with rational vertex coordinates and let R(u) be a rectangle with side lengths u and 1. An orthogonal polygon P can be tiled with similar copies of R(u) if and only if u is alge
Local systems of vertex operators, vertex superalgebras and modules
"... We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators ” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a n ..."
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Cited by 168 (34 self)
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lowest weight modules for some wellknown infinitedimensional Lie algebras or Lie superalgebras have natural vertex operator superalgebra structures. We prove the rationality of vertex operator superalgebras associated to standard modules for an affine algebra. We also give an analogue of the notion
Regularity of rational vertex operator algebras
"... Rational vertex operator algebras, which play a fundamental role in rational conformal field theory (see [BPZ] and [MS]), single out an important class of vertex operator algebras. Most vertex operator algebras which have been studied so far are rational vertex operator ..."
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Cited by 113 (65 self)
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Rational vertex operator algebras, which play a fundamental role in rational conformal field theory (see [BPZ] and [MS]), single out an important class of vertex operator algebras. Most vertex operator algebras which have been studied so far are rational vertex operator
Rationality of Virasoro vertex operator algebras
 Duke Math. J. IMRN
, 1993
"... Vertex operator algebras (VOA) were introduced by Borcherds ( [B] ) as an axiomatic ..."
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Cited by 87 (0 self)
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Vertex operator algebras (VOA) were introduced by Borcherds ( [B] ) as an axiomatic
SOME RATIONAL VERTEX ALGEBRAS
, 1998
"... ... 2)Λ0), n ∈ N, be a vertex operator algebra associated to the irreducible highest weight module L((n − 3 2)Λ0) for a symplectic affine Lie algebra. We find a complete set of irreducible modules for L((n − 3 2)Λ0) and show that every module for L((n − 3 2)Λ0) from the category O is completely redu ..."
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Cited by 15 (3 self)
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... 2)Λ0), n ∈ N, be a vertex operator algebra associated to the irreducible highest weight module L((n − 3 2)Λ0) for a symplectic affine Lie algebra. We find a complete set of irreducible modules for L((n − 3 2)Λ0) and show that every module for L((n − 3 2)Λ0) from the category O is completely
Rationality of vertex operator algebras
, 2006
"... It is shown that a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is semisimple and each irreducible admissible Vmodule is ordinary. A contravariant form on a Verma type admissible Vmodule is constructed and the radical is exactly the maximal proper submodule. As ..."
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Cited by 2 (0 self)
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It is shown that a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is semisimple and each irreducible admissible Vmodule is ordinary. A contravariant form on a Verma type admissible Vmodule is constructed and the radical is exactly the maximal proper submodule
Rational vertex operator algebras and the effective central charge
"... We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank l is bounded above by the effective central charge ˜c. We show that lattice vertex operator algebras may be characterized by the equalities ˜c = l = c, and in p ..."
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Cited by 40 (26 self)
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We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank l is bounded above by the effective central charge ˜c. We show that lattice vertex operator algebras may be characterized by the equalities ˜c = l = c
Results 1  10
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283