کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4667693 1345474 2007 40 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces
چکیده انگلیسی

In this paper the representation theory of 2-groups in 2-categories is considered, focusing the attention on the 2-category Rep2MatK(G) of representations of a 2-group G in (a version of) Kapranov and Voevodsky's 2-category of 2-vector spaces over a field K. The set of equivalence classes of such representations is computed in terms of the invariants π0(G), π1(G) and [α]∈H3(π0(G),π1(G)) classifying G, and the categories of intertwiners are described in terms of categories of vector bundles endowed with a projective action. In particular, it is shown that the monoidal category of finite dimensional linear representations (more generally, the category of [z]-projective representations, for any given cohomology class [z]∈H2(π0(G),K∗)) of the first homotopy group π0(G) as well as its category of representations on finite sets both live in Rep2MatK(G), the first as the monoidal category of endomorphisms of the trivial representation (more generally, as the category of intertwiners between suitable 1-dimensional representations) and the second as a non-full subcategory of the homotopy category of Rep2MatK(G).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 213, Issue 1, 1 August 2007, Pages 53-92