کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587798 1334159 2008 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Double Poisson cohomology of path algebras of quivers
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Double Poisson cohomology of path algebras of quivers
چکیده انگلیسی

In this note, we give a description of the graded Lie algebra of double derivations of a path algebra as a graded version of the necklace Lie algebra equipped with the Kontsevich bracket. Furthermore, we formally introduce the notion of double Poisson–Lichnerowicz cohomology for double Poisson algebras, and give some elementary properties. We introduce the notion of a linear double Poisson tensor on a quiver and show that it induces the structure of a finite-dimensional algebra on the vector spaces Vv generated by the loops in the vertex v. We show that the Hochschild cohomology of the associative algebra can be recovered from the double Poisson cohomology. Then, we use the description of the graded necklace Lie algebra to determine the low-dimensional double Poisson–Lichnerowicz cohomology groups for three types of (linear and nonlinear) double Poisson brackets on the free algebra C〈x,y〉. This allows us to develop some useful techniques for the computation of the double Poisson–Lichnerowicz cohomology.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 319, Issue 5, 1 March 2008, Pages 2166-2208