Symmetry of Lie algebras associated with (ε, δ)-Freudenthal-Kantor triple system

Kamiya, Noriaki; Ôkubo, Susumu

doi:10.1017/s0013091514000406

Cited by 4 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section we would like to discuss an interesting connection between the Govorkov trilinear relations (3.1) -(3.3) and so-called Lie-supertriple system. The Lie-supertriple system, which is a generalization of the standard Lie-triple system [35][36][37][38], was studied in detail in the works of Okubo et al [39][40][41][42]. Our consideration will be based on the work [39], in which the author has reformulated the parastatistics as a Lie-supertriple system.…”

Section: Lie-supertriple Systemmentioning

confidence: 99%

Unitary Quantization and Para-Fermi Statistics of Order 2

Markov

Markova

Гитман

2018

J. Exp. Theor. Phys.

View full text Add to dashboard Cite

A connection between a unitary quantization scheme and para-Fermi statistics of order 2 is considered. An appropriate extension of Green's ansatz is suggested. This extension allows one to transform bilinear and trilinear commutation relations for the annihilation and creation operators of two different para-Fermi fields φ a and φ b into identity. The way of incorporating para-Grassmann numbers ξ k into a general scheme of uniquantization is also offered. For parastatistics of order 2 a new fact is revealed, namely, the trilinear relations containing both the para-Grassmann variables ξ k and the field operators a k , b m under a certain invertible mapping go over into the unitary equivalent relations, where commutators are replaced by anticommutators and vice versa. It is shown that the consequence of this circumstance is the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green's components of the operators a k , b m is constructed in an explicit form that enables us to reduce the initial commutation rules for the components to the normal commutation relations of ordinary Fermi fields. A nontrivial connection between trilinear commutation relations of the unitary quantization scheme and so-called Lie-supertriple system is analysed. A brief discussion of the possibility of embedding the Duffin-Kemmer-Petiau theory into the unitary quantization scheme is provided. *

show abstract

Section: Lie-supertriple Systemmentioning

confidence: 99%

Unitary Quantization and Para-Fermi Statistics of Order 2

Markov

Markova

Гитман

2018

J. Exp. Theor. Phys.

View full text Add to dashboard Cite

show abstract

On Certain Algebraic Structures Associated with Lie (Super)Algebras

Kamiya

2023

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms

Kamiya

Mondoc

2019

J. Algebra Appl.

View full text Add to dashboard Cite

In this work, we discuss a classification of [Formula: see text]-Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these ([Formula: see text]-Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.

show abstract

Symmetry of Lie algebras associated with (ε, δ)-Freudenthal-Kantor triple system

Cited by 4 publications

References 16 publications

Unitary Quantization and Para-Fermi Statistics of Order 2

Unitary Quantization and Para-Fermi Statistics of Order 2

On Certain Algebraic Structures Associated with Lie (Super)Algebras

On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms

Contact Info

Product

Resources

About