Alternative Definitions
Another way to think of vertex algebras is as a generalisation of a Lie algebra with the addition of a continuous variable to both the generators of the algebra and the structure constant. (The structure constants define the algebra). So we would have:
which can also be expressed without the y dependence as:
which reveals the Vertex Multiplication as a group operation in which the group constants vary with their position on the conformal sheet.
Read more about this topic: Vertex Operator Algebra
Famous quotes containing the words alternative and/or definitions:
“If English is spoken in heaven ... God undoubtedly employs Cranmer as his speechwriter. The angels of the lesser ministries probably use the language of the New English Bible and the Alternative Service Book for internal memos.”
—Charles, Prince Of Wales (b. 1948)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)