A Course in Vertex Algebra
| dc.creator | Rosellen, Markus | |
| dc.date | 2006-07-12 | |
| dc.date.accessioned | 2026-07-07T07:18:16Z | |
| dc.date.available | 2026-07-07T07:18:16Z | |
| dc.description | This book offers an introduction to vertex algebra based on a new approach. The new approach says that a vertex algebra is an associative algebra such that the underlying Lie algebra is a vertex Lie algebra. In particular, vertex algebras can be formulated in terms of a single multiplication and they behave like associative algebras with respect to it. Chapter 1 is the introduction. In chapter 2 we discuss many examples of vertex Lie algebras and we show that vertex Lie algebras form a full subcategory of the category of "local" Lie algebras. In chapter 3 we introduce associative, commutative, and Poisson vertex algebras and vertex algebra modules and we show that graded associative vertex algebras form a full subcategory of the category of "local" associative algebras. In chapter 4 we give a systematic presentation of the vertex algebra identities, proving in particular the equivalence of various axiom systems, and we use filtrations to prove results about generating subspaces with the PBW-property, with and without repeats. In chapter 5 we explain three constructions of the enveloping vertex algebra of a vertex Lie algebra and prove the PBW-theorem. In chapter 6 we prove the Zhu correspondence between N-graded vertex algebra modules and modules over the Zhu algebra. | |
| dc.description | book, 204+x pages, comments are welcome | |
| dc.identifier | https://arxiv.org/abs/math/0607270 | |
| dc.identifier | http://arxiv.org/abs/math/0607270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114235 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17B69 | |
| dc.title | A Course in Vertex Algebra | |
| dc.type | text |