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
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

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
Journal: Journal of Algebra - Volume 391, 1 October 2013, Pages 152-192
نویسندگان
Victoria Lebed,