GENERIC JORDAN TYPE OF THE SYMMETRIC AND EXTERIOR POWERS

Journal of Algebra and Its Applications ◽

10.1142/s0219498813501636 ◽

2014 ◽

Vol 13 (05) ◽

pp. 1350163 ◽

Author(s):

DAVID J. BENSON ◽

KAY JIN LIM

Keyword(s):

Jordan Type ◽

Trivial Module ◽

Exterior Powers

We prove a result relating the stable generic Jordan types of the symmetric and exterior powers of the Heller translations of a module for a finite elementary abelian p-group. In the case of the trivial module, the stable generic Jordan types of the symmetric and exterior powers of its Heller translations are completely described.

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Polynomial ring representations of endomorphisms of exterior powers

Collectanea mathematica ◽

10.1007/s13348-020-00310-5 ◽

2021 ◽

Author(s):

Ommolbanin Behzad ◽

André Contiero ◽

Letterio Gatto ◽

Renato Vidal Martins

Keyword(s):

Lie Algebra ◽

Polynomial Ring ◽

Vertex Operators ◽

Exterior Power ◽

Infinite Dimensional ◽

Symmetric Structure ◽

Rational Polynomials ◽

Exterior Powers ◽

Vertex Representation ◽

Countably Infinite

AbstractAn explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.

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Pseudo-atoms, atoms and a Jordan type decomposition in effect algebras

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2008.03.003 ◽

2008 ◽

Vol 344 (1) ◽

pp. 238-252 ◽

Author(s):

Mona Khare ◽

Akhilesh Kumar Singh

Keyword(s):

Effect Algebras ◽

Jordan Type ◽

Type Decomposition

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Absolutely (completely) monotonic functions and Jordan-type inequalities

Applied Mathematics Letters ◽

10.1016/j.aml.2011.09.061 ◽

2012 ◽

Vol 25 (3) ◽

pp. 571-574 ◽

Author(s):

Shijun Yang

Keyword(s):

Jordan Type ◽

Monotonic Functions ◽

Completely Monotonic ◽

Completely Monotonic Functions

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Exterior powers

Abstract Algebra ◽

10.1201/b15896-30 ◽

2007 ◽

pp. 429-458

Keyword(s):

Exterior Powers

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Modules of Constant Jordan Type

Representations of Elementary Abelian p-Groups and Vector Bundles ◽

10.1017/9781316795699.007 ◽

2017 ◽

pp. 89-128

Author(s):

David J. Benson

Keyword(s):

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Finitely presented groups and the finite generation of exterior powers

Combinatorial and Geometric Group Theory, Edinburgh 1993 ◽

10.1017/cbo9780511566073.003 ◽

1994 ◽

pp. 16-28

Author(s):

C J B Brookes

Keyword(s):

Finite Generation ◽

Finitely Presented Groups ◽

Exterior Powers ◽

Finitely Presented

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On primitive 3-generated axial algebras of Jordan type

Journal of Algebra ◽

10.1016/j.jalgebra.2020.07.014 ◽

2020 ◽

Vol 563 ◽

pp. 74-99

Author(s):

Ilya Gorshkov ◽

Alexey Staroletov

Keyword(s):

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Decomposable Tensors in Exterior Powers

Hasse-Schmidt Derivations on Grassmann Algebras ◽

10.1007/978-3-319-31842-4_6 ◽

2016 ◽

pp. 121-146

Author(s):

Letterio Gatto ◽

Parham Salehyan

Keyword(s):

Exterior Powers

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p-Power Points and Modules of Constantp-Power Jordan Type

Communications in Algebra ◽

10.1080/00927872.2010.512585 ◽

2011 ◽

Vol 39 (10) ◽

pp. 3781-3800 ◽

Author(s):

Semra Öztürk Kaptanoğlu

Keyword(s):

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A further refinement of a Jordan type inequality and its application

Applied Mathematics and Computation ◽

10.1016/j.amc.2007.08.022 ◽

2008 ◽

Vol 197 (2) ◽

pp. 914-923 ◽

Author(s):

Shan-He Wu ◽

H.M. Srivastava

Keyword(s):

Type Inequality ◽

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