Nilpotent Lie algebras of breadth type (0,3)

被引：1

作者：

Kundu, Rijubrata ^{[1
,4
]}

Naik, Tushar Kanta ^{[2
]}

Singh, Anupam ^{[3
]}

机构：

[1] Indian Inst Sci Educ & Res Mohali, Mohali, India

[2] Natl Inst Sci Educ & Res, OCC Homi Bhabha Natl Inst, Sch Math Sci, Bhubaneswar, Orissa, India

[3] Indian Inst Sci Educ & Res Pune, Pune, India

[4] Indian Inst Sci Educ & Res Mohali, Sect 81, Mohali 140306, India

来源：

COMMUNICATIONS IN ALGEBRA | 2023年 / 51卷 / 09期

关键词：

Breadth type; Camina Lie algebras; nilpotent Lie algebras; REAL LINEAR-COMBINATIONS; FINITE P-GROUPS; CLASSIFICATION; MATRICES; FIELDS;

D O I：

10.1080/00927872.2023.2188416

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a natural number m, a Lie algebra L over a field k is said to be of breadth type (0,m) if the co-dimension of the centralizer of every non-central element is m. In this article, we classify finite dimensional nilpotent Lie algebras of breadth type (0,3) over F-q of odd characteristic up to isomorphism. We also give a partial classification of the same over finite fields of even characteristic, C and R. We also discuss 2-step nilpotent Camina Lie algebras.

引用

页码：3792 / 3809

页数：18

共 29 条

[21] Finite p-Groups of Nilpotency Class 3 with Two Conjugacy Class Sizes
Naik, Tushar Kanta
Kitture, Rahul Dattatraya
Yadav, Manoj K.
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2020, 236 (02) : 899 - 930
[22] Finite p-groups of conjugate type {1, p3}
Naik, Tushar Kanta
Yadav, Manoj K.
[J]. JOURNAL OF GROUP THEORY, 2018, 21 (01) : 65 - 82
[23] p-Groups of small breadth
Parmeggiani, G
Stellmacher, B
[J]. JOURNAL OF ALGEBRA, 1999, 213 (01) : 52 - 68
[24] Radon J., 1922, ABH MATH SEM HAMBURG, V1, P1, DOI 10.1007/BF02940576
[25] Breadth and characteristic sequence of nilpotent Lie algebras
Remm, Elisabeth
[J]. COMMUNICATIONS IN ALGEBRA, 2017, 45 (07) : 2956 - 2966
[26] 7-DIMENSIONAL NILPOTENT LIE-ALGEBRAS
SEELEY, C
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 335 (02) : 479 - 496
[27] Sheikh-Mohseni S., 2018, ASIAN-EUR J MATH, V11, p1850063, 11
[28] Characterization of nilpotent Lie algebras of breadth 3 over finite fields of odd characteristic
Sriwongsa, Songpon
Wiboonton, Keng
Khuhirun, Borworn
[J]. JOURNAL OF ALGEBRA, 2021, 586 : 935 - 972
[29] 2-groups of breadth 3
Wilkens, B.
[J]. JOURNAL OF ALGEBRA, 2007, 318 (01) : 202 - 224

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