کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897410 | 1630739 | 2018 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Current superalgebras and unitary representations
ترجمه فارسی عنوان
معادلات جاری و نمایندگی های واحد
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
In this paper we determine the projective unitary representations of finite dimensional Lie supergroups whose underlying Lie superalgebra is g=Aâk, where k is a compact simple Lie superalgebra and A is a supercommutative associative (super)algebra; the crucial case is when A=Îs(R) is a GraÃmann algebra. Since we are interested in projective representations, the first step consists in determining the cocycles defining the corresponding central extensions. Our second main result asserts that, if k is a simple compact Lie superalgebra with k1â {0}, then each (projective) unitary representation of Îs(R)âk factors through a (projective) unitary representation of k itself, and these are known by Jakobsen's classification. If k1={0}, then we likewise reduce the classification problem to semidirect products of compact Lie groups K with a Clifford-Lie supergroup which has been studied by Carmeli, Cassinelli, Toigo and Varadarajan.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 10, October 2018, Pages 3303-3333
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 10, October 2018, Pages 3303-3333
نویسندگان
Karl-Hermann Neeb, Malihe Yousofzadeh,