A Note on the Schur Multiplier of a Nilpotent Lie Algebra

Niroomand, Peyman; Russo, Francesco G.

doi:10.1080/00927871003652660

Cited by 53 publications

(73 citation statements)

References 9 publications

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“…A similar parallel is possible, when we compare [9,Main Theorem] with [13,Theorem 3.1]. Therefore, we get to the subject of the present paper: we improve [13, Theorem 3.1], overlapping a situation for p-groups with large derived subgroup, recently investigated in [10].…”

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 64%

“…In fact, the reader may compare Proposition 2.3 and Theorem 3.1 below with [3, Theorems 10 and 12]. Now some general considerations are recalled from [13].…”

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

“…Assigned t(L) = [1,2,5,8,13,18], which are devoted to detect the structure of L, when values of t(L) higher than 2 are considered. On another hand, [1,2,5,8,13,18] deal with bounds on dim(M (L)) and sometimes it is possible to adapt these bounds in order to study other important constructions of topology and K-theory, investigated in [4,11,12,16], where restrictions on the second homology group are involved.…”

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

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A restriction on the Schur multiplier of nilpotent Lie algebras

Niroomand¹,

Russo

2011

ELA

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Abstract. An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M (L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maximal dimension. This allows precision on the size of M (L). Among other results, applications to the non-abelian tensor square L ⊗ L are illustrated.

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Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 64%

“…In fact, the reader may compare Proposition 2.3 and Theorem 3.1 below with [3, Theorems 10 and 12]. Now some general considerations are recalled from [13].…”

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

See 1 more Smart Citation

A restriction on the Schur multiplier of nilpotent Lie algebras

Niroomand¹,

Russo

2011

ELA

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“…Later, Niroomand and Parvizi in [4] classified all capable p-groups with commutator subgroup of order p and the abelianization of groups in term of its Schur multiplier, epicenter and exterior square. In 2012, the capability of groups of order 2 p q has been computed by Samad et al in [5].…”

Section: Z G Z E E Gmentioning

confidence: 99%

On the capability of nonabelian groups of order p4

Zainal

Ali²,

Sarmin³

et al. 2014

AIP Conference Proceedings

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Non-Abelian point group symmetry in direct second-order many-body perturbation theory calculations of NMR chemical shifts Abstract. A group is capable if it is isomorphic to the central factor group. For finite groups of prime power order, the capability is closely related to their classification. In this research, by using the classification of groups of order p 4 , we determine the capability of this group.

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“…Similarly, for the case c = 1, the abelian Lie algebra M(L) = M (1) (L) is more studied by the first author and the others (see for instance [4,5,6,8,9,10,15,16,17,24]). …”

Section: Introductionmentioning

confidence: 99%

2-capability and 2-nilpotent multiplier of finite dimensional nilpotent Lie algebras

Niroomand

Parvizi

2017

Journal of Geometry and Physics

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Abstract. In the present context, we investigate to obtain some more results about 2-nilpotent multiplier M (2) (L) of a finite dimensional nilpotent Lie algebra L. For instance, we characterize the structure of M (2) (H) when H is a Heisenberg Lie algebra. Moreover, we give some inequalities on dim M (2) (L) to reduce a well known upper bound on 2-nilpotent multiplier as much as possible. Finally, we show that H(m) is 2-capable if and only if m=1.

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A Note on the Schur Multiplier of a Nilpotent Lie Algebra

Abstract: For a nilpotent Lie algebra L of dimension n and dim(where M (L) denotes the Schur multiplier of L. In case m = 1 the equality holds if and only if L ∼ = H(1) ⊕ A, where A is an abelian Lie algebra of dimension n − 3 and H(1) is the Heisenberg algebra of dimension 3.

Cited by 53 publications

References 9 publications

A restriction on the Schur multiplier of nilpotent Lie algebras

A restriction on the Schur multiplier of nilpotent Lie algebras

On the capability of nonabelian groups of order p4

2-capability and 2-nilpotent multiplier of finite dimensional nilpotent Lie algebras

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