Split Casimir Operator of Algebra $$D(2,1;\alpha )$$ in Representations $$a{{d}^{{ \otimes 2}}}$$ and $$a{{d}^{{ \otimes 3}}}$$ and Vogel Parameterization

IF 0.4 Q4 PHYSICS, PARTICLES & FIELDS Physics of Particles and Nuclei Letters Pub Date : 2024-08-14 DOI:10.1134/s1547477124700894

A. A. Provorov

引用次数: 0

Abstract

Characteristic identities for $2$- and $3$-split Casimir algebra operators $D(2,1;\alpha )$ in representations $a{{d}^{{ \otimes 2}}}$ and $a{{d}^{{ \otimes 3}}}$ are found; projectors onto the invariant subspaces of these representations are constructed, and formulas for their supertraces are derived. All formulas agree with the universal description of subrepresentations of representations $a{{d}^{{ \otimes 2}}}$ and $a{{d}^{{ \otimes 3}}}$ of basic classical Lie superalgebras in terms of Vogel parameters.

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代数$$D(2,1;\alpha )$$在表示$$a{{d}^{ \otimes 2}}}$$和$$a{{d}^{ \otimes 3}}}$$中的分裂卡西米尔算子以及沃格尔参数化

Abstract 发现了在表示 $a{{d}^{ \otimes 2}}$ 和 $a{{d}^{ \otimes 3}}$ 中 $2$- 和 $3$- 分裂卡西米尔代数算子 $D(2,1;\alpha )$ 的特征同位；构造了这些表示的不变子空间的投影，并推导出了它们的超线公式。所有公式都与用 Vogel 参数对基本经典李超拉的 \(a{{d}^{ \otimes 2}}} 和 \(a{{d}^{ \otimes 3}}}) 表示的子表示的普遍描述一致。

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来源期刊

Physics of Particles and Nuclei Letters PHYSICS, PARTICLES & FIELDS-

CiteScore

0.80

自引率

20.00%

发文量

108

期刊介绍： The journal Physics of Particles and Nuclei Letters, brief name Particles and Nuclei Letters, publishes the articles with results of the original theoretical, experimental, scientific-technical, methodological and applied research. Subject matter of articles covers: theoretical physics, elementary particle physics, relativistic nuclear physics, nuclear physics and related problems in other branches of physics, neutron physics, condensed matter physics, physics and engineering at low temperatures, physics and engineering of accelerators, physical experimental instruments and methods, physical computation experiments, applied research in these branches of physics and radiology, ecology and nuclear medicine.