کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4584383 1630489 2015 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The geometry of finite dimensional algebras with vanishing radical square
ترجمه فارسی عنوان
هندسه جبرهای بعدی محدود با ناپدید شدن مربع رادیکال؟
کلمات کلیدی
نمایه های جبری محدود بعدی، اجزاء غیر قابل تحمل از انواع پارامتریزه کردن، خواص عمومی نمایندگی ها
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Let Λ be a basic finite dimensional algebra over an algebraically closed field, with the property that the square of the Jacobson radical J   vanishes. We determine the irreducible components of the module variety Repd(Λ)Repd(Λ) for any dimension vector d. Our description leads to a count of the components in terms of the underlying Gabriel quiver. A closed formula for the number of components when Λ is local extends existing counts for the two-loop quiver to quivers with arbitrary finite sets of loops.For any algebra Λ   with J2=0J2=0, our criteria for identifying the components of Repd(Λ)Repd(Λ) permit us to characterize the modules parametrized by the individual irreducible components. Focusing on such a component, we explore generic properties of the corresponding modules by establishing a geometric bridge between the algebras with zero radical square on the one hand and their stably equivalent hereditary counterparts on the other. The bridge links certain closed subvarieties of Grassmannians parametrizing the modules with fixed top over the two types of algebras. By way of this connection, we transfer results of Kac and Schofield from the hereditary case to algebras of Loewy length 2. Finally, we use the transit of information to show that any algebra of Loewy length 2 which enjoys the dense orbit property in the sense of Chindris, Kinser and Weyman has finite representation type.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 425, 1 March 2015, Pages 146–178
نویسندگان
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