In 1998 P. Etingof and D. Kazhdan defined the notion of quantum vertex algebra. They started from the definition of vertex algebra and they replaced the underlying vector space with a topologically free K[[h]]-module, then they deformed the locality introducing a braiding map which is a solution of the quantum Yang-Baxter equation. Since the obtained object, called braided vertex algebra, doesn't satisfy the associativity relation they imposed an additional axiom called "Hexagon relation" which implies the associativity relation. In their foundational article, P. Etingof and D. Kazhdan gave also a nontrivial example of quantum vertex algebra: the quantum affine vertex algebra. In the first part of our work we study the notion of S-commutative braided vertex algebras which satisfy the associativity relation, we give a characterization of braided vertex algebras which satisfy the associativity relation and we prove in every detail that the example given by P. Etingof and D. Kazhdan satisfies all the axioms of a quantum vertex algebra. In the second part we deal with Drinfeld's notes on universal triangular R-matrices.
Quantum vertex algebras / Gardini, Matteo. - (2019 Jan 29).
Quantum vertex algebras
Gardini, Matteo
29/01/2019
Abstract
In 1998 P. Etingof and D. Kazhdan defined the notion of quantum vertex algebra. They started from the definition of vertex algebra and they replaced the underlying vector space with a topologically free K[[h]]-module, then they deformed the locality introducing a braiding map which is a solution of the quantum Yang-Baxter equation. Since the obtained object, called braided vertex algebra, doesn't satisfy the associativity relation they imposed an additional axiom called "Hexagon relation" which implies the associativity relation. In their foundational article, P. Etingof and D. Kazhdan gave also a nontrivial example of quantum vertex algebra: the quantum affine vertex algebra. In the first part of our work we study the notion of S-commutative braided vertex algebras which satisfy the associativity relation, we give a characterization of braided vertex algebras which satisfy the associativity relation and we prove in every detail that the example given by P. Etingof and D. Kazhdan satisfies all the axioms of a quantum vertex algebra. In the second part we deal with Drinfeld's notes on universal triangular R-matrices.File | Dimensione | Formato | |
---|---|---|---|
Tesi_dottorato_Gardini.pdf
accesso aperto
Tipologia:
Tesi di dottorato
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
934.63 kB
Formato
Adobe PDF
|
934.63 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.