کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598009 1336245 2008 57 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Representations of centrally-extended Lie algebras over differential operators and vertex algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Representations of centrally-extended Lie algebras over differential operators and vertex algebras
چکیده انگلیسی

We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries. The structures of vertex algebras associated with the vacuum representations of these algebras are determined. Moreover, we prove that under certain conditions, the highest-weight irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries naturally give rise to the irreducible modules of the simple quotients of these vertex algebras. From vertex algebra and its representation point of view, our results with positive integral central charge are high-order differential operator analogues of the well-known WZW models in conformal field theory associated with affine Kac–Moody algebras. Indeed, when the left ideals are the algebra of differential operators, our Lie algebras do contain affine Kac–Moody algebras as subalgebras and our results restricted on them are exactly the representation contents in WZW models. Similar results with negative central charge are also obtained.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 212, Issue 6, June 2008, Pages 1253–1309
نویسندگان
,