scholarly journals A Classification of Lie Algebras of Pseudo-Unitary Groups in the Techniques of Clifford Algebras

2009 ◽  
Vol 20 (2) ◽  
pp. 411-425 ◽  
Author(s):  
D. S. Shirokov
Keyword(s):  
Lie Algebras ◽  
Clifford Algebras ◽  
Unitary Groups

Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices

2006 ◽  
Vol 13 (04) ◽  
pp. 415-426 ◽  
Author(s):  
P. Aniello ◽  
C. Lupo ◽  
M. Napolitano
Keyword(s):  
Lie Algebras ◽  
Fock Space ◽  
Fixed Number ◽  
Unitary Groups ◽  
Space Representation ◽  
Remarkable Case ◽  
Mathematical Structures ◽  
Passive Devices ◽  
Optical Modes ◽  
Linear Optical

In this paper, we investigate some mathematical structures underlying the physics of linear optical passive (LOP) devices. We show, in particular, that with the class of LOP transformations on N optical modes one can associate a unitary representation of U (N) in the N-mode Fock space, representation which can be decomposed into irreducible sub-representations living in the subspaces characterized by a fixed number of photons. These (sub-)representations can be classified using the theory of representations of semi-simple Lie algebras. The remarkable case where N = 3 is studied in detail.

scholarly journals Capable n-Lie algebras and the classification of nilpotent n-Lie algebras with s(A)=3

2016 ◽  
Vol 110 ◽  
pp. 25-29 ◽  
Author(s):  
Hamid Darabi ◽  
Farshid Saeedi ◽  
Mehdi Eshrati
Keyword(s):  
Lie Algebras

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

Complete classification of pseudo H-type Lie algebras: I

2017 ◽  
Vol 190 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Kenro Furutani ◽  
Irina Markina
Keyword(s):  
Lie Algebras ◽  
Complete Classification

scholarly journals On classification of (n+6)-dimensional nilpotent n-Lie algebras of class 2 with n≥4

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehdi Jamshidi ◽  
Farshid Saeedi ◽  
Hamid Darabi
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Design Methodology ◽  
Central Element ◽  
Complete Understanding ◽  
Content Type ◽  
Low Dimension

PurposeThe purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4.Design/methodology/approachBy dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras.FindingsIn this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras.Originality/valueThis classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

scholarly journals k-step nilpotent Lie algebras

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Michel Goze ◽  
Elisabeth Remm
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Deformation Process ◽  
Nilpotent Lie Algebras ◽  
Early Stages ◽  
Finite Dimensional ◽  
Contraction Process ◽  
Finite Dimensional Lie Algebras

AbstractThe classification of complex or real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example, the nilpotent Lie algebras are classified only up to dimension 7. Moreover, to recognize a given Lie algebra in the classification list is not so easy. In this work, we propose a different approach to this problem. We determine families for some fixed invariants and the classification follows by a deformation process or a contraction process. We focus on the case of 2- and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology for this type of algebras and the algebras which are rigid with respect to this cohomology. Other

A classification of subgroups of odd unitary groups

2018 ◽  
Vol 46 (9) ◽  
pp. 3795-3805 ◽  
Author(s):  
Weibo Yu ◽  
Yaya Li ◽  
Hang Liu
Keyword(s):  
Unitary Groups
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