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Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
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RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.33 no.s2 (2006), pp. 3-25
Generalized Vertex Algebras
B. Bakalov1, V.G. Kac2
1Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA
2Department of Mathematics, MIT, Cambridge, MA 02139, USA
go back1Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA
2Department of Mathematics, MIT, Cambridge, MA 02139, USA
Abstract. We give a short introduction to generalized vertex algebras, using the notion of polylocal fields. We construct a generalized vertex algebra associated to a vector space h with a symmetric bilinear form. It contains as subalgebras all lattice vertex algebras of rank equal to dim h and all irreducible representations of these vertex algebras.