Generalized Canonical Isomorphisms on Determinant  

作　　者：Jianke Chen 

机构地区：[1]Department of Mathematics, Communication University of China Beijing 100024, China

出　　处：《Algebra Colloquium》2016年第2期239-242,共4页代数集刊（英文版）

摘　　要：In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we give a series of tensor modules （sheaves） of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules （sheaves） of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we give a series of tensor modules （sheaves） of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules （sheaves） of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.

关 键 词：tensor sheaves of Schur types generalized canonical isomorphism on determinant 

分 类 号：O157.5[理学—数学] TF31[理学—基础数学]