کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4585050 1630523 2013 41 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homologies of algebraic structures via braidings and quantum shuffles
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Homologies of algebraic structures via braidings and quantum shuffles
چکیده انگلیسی
In this paper we construct “structural” pre-braidings characterizing different algebraic structures: a rack, an associative algebra, a Leibniz algebra and their representations. Some of these pre-braidings seem original. On the other hand, we propose a general homology theory for pre-braided vector spaces and braided modules, based on the quantum co-shuffle comultiplication. Applied to the structural pre-braidings above, it gives a generalization and a unification of many known homology theories. All the constructions are categorified, resulting in particular in their super- and co-versions. Lodayʼs hyper-boundaries, as well as certain homology operations are efficiently treated using the “shuffle” tools.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 391, 1 October 2013, Pages 152-192
نویسندگان
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