کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6414461 1630491 2015 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
LDB division algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
LDB division algebras
چکیده انگلیسی

An LDB division algebra is a triple (A,⋆,
- ) in which ⋆ and
- are regular bilinear laws on the finite-dimensional non-zero vector space A such that x⋆(x
- y) is a scalar multiple of y for all vectors x and y of A. This algebraic structure has been recently discovered in the study of the critical case in Meshulam and Å emrl's estimate of the minimal rank in non-reflexive operator spaces.In this article, we obtain a constructive description of all LDB division algebras over an arbitrary field together with a reduction of the isotopy problem to the similarity problem for specific types of quadratic forms over the given field. In particular, it is shown that the dimension of an LDB division algebra is always a power of 2, and that it belongs to {1,2,4,8} if the characteristic of the underlying field is not 2.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 423, 1 February 2015, Pages 259-288
نویسندگان
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