Canonical bilinear form and Euler characters
نویسندگان
چکیده
An explicit formula for the canonical bilinear form on Grothendieck ring of Lie supergroup G L ( n , m ) is given. As an application we get algorithm decomposition Euler characters in terms irreducible modules category partially polynomial modules.
منابع مشابه
Canonical matrices of bilinear and sesquilinear forms
Canonical matrices are given for • bilinear forms over an algebraically closed or real closed field; • sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and • sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of...
متن کاملJordan Canonical Form
is the geometric multiplicity of λk which is also the number of Jordan blocks corresponding to λk . • The orders of the Jordan Blocks of λk must sum to the algebraic multiplicity of λk . • The number of Jordan blocks corresponding to an eigenvalue λk is its geometric multiplicity. • The matrix A is diagonalizable if and only if, for any eigenvalue λ of A , its geometric and algebraic multiplici...
متن کاملThe Jordan Canonical Form
Let β1, . . . , βn be linearly independent vectors in a vector space. For all j with 0 ≤ j ≤ n and all vectors α1, . . . , αk, if β1, . . . , βn are in the span of β1, . . . , βj, α1, . . . , αk, then j + k ≥ n. The proof of the claim is by induction on k. For k = 0, the claim is obvious since β1, . . . , βn are linearly independent. Suppose the claim is true for k−1, and suppose that β1, . . ....
متن کاملThe Canonical Contact Form
The structure group and the involutive differential system that characterize the pseudo-group of contact transformations on a jet space are determined.
متن کاملRational Canonical Form
In mathematics, complete classification of structures, such as groups and rings, is often a primary goal. Linear transformations are no exception to this. Certain canonical forms exist to classify linear transformations, therefore creating a unique representative of linear transformations in the same similarity class. Diagonal representation is of course one of the simplest examples of a canoni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.02.014