scholarly journals Some upper bounds for the dimension of the c-nilpotent multiplier of a pair of Lie algebras

2020 ◽  
Vol 40 (2) ◽  
pp. 159
Author(s):  
Homayoon Arabyani ◽  
Mohammad Javad Sadeghifard ◽  
Sedigheh Sheikh-Mohseni
Keyword(s):  
Lie Algebras ◽  
Upper Bounds ◽  
Pair Of Lie Algebras

scholarly journals Capability and Schur multiplier of a pair of Lie algebras

2017 ◽  
Vol 114 ◽  
pp. 184-196 ◽  
Author(s):  
Farangis Johari ◽  
Mohsen Parvizi ◽  
Peyman Niroomand
Keyword(s):  
Lie Algebras ◽  
Schur Multiplier ◽  
Pair Of Lie Algebras

On c-nilpotent multiplier and c-covers of a pair of Lie algebras

2016 ◽  
Vol 45 (10) ◽  
pp. 4429-4434 ◽  
Author(s):  
Hesam Safa ◽  
Homayoon Arabyani
Keyword(s):  
Lie Algebras ◽  
Pair Of Lie Algebras

SOME PROPERTIES ON THE SCHUR MULTIPLIER OF A PAIR OF LIE ALGEBRAS

2012 ◽  
Vol 11 (01) ◽  
pp. 1250011 ◽  
Author(s):  
MOHAMMAD REZA RISMANCHIAN ◽  
MEHDI ARASKHAN
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Central Extension ◽  
Sufficient Condition ◽  
Schur Multiplier ◽  
Necessary And Sufficient Condition ◽  
Pair Of Lie Algebras ◽  
Necessary And Sufficient

The aim of this paper is to introduce the concept of the Schur multiplier [Formula: see text] of a pair of Lie algebras and to obtain some inequalities for the dimension of [Formula: see text]. Also, we consider some of the features of central extension of an arbitrary Lie algebra. Moreover, we present a necessary and sufficient condition in which the Schur multiplier of a pair of Lie algebras can be embedded into the Schur multiplier of their factor Lie algebras.

scholarly journals Matched pairs of Lie algebroids

1997 ◽  
Vol 39 (2) ◽  
pp. 167-181 ◽  
Author(s):  
Tahar Mokri
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Algebroids ◽  
Matched Pair ◽  
Matched Pairs ◽  
Lie Groupoids ◽  
Pair Of Lie Algebras

AbstractWe extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras (Kosmann-Schwarzbach and Magri). It is proved that a matched pair of Lie groupoids induces a matched pair of Lie algebroids. Conversely, we show that under certain conditions a matched pair of Lie algebroids integrates to a matched pair of Lie groupoids. The importance of matched pairs of Lie algebroids has been recently demonstrated by Lu.

Some properties of c-covers of a pair of Lie algebras

2018 ◽  
Vol 42 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Homayoon Arabyani ◽  
Hesam Safa
Keyword(s):  
Lie Algebras ◽  
Pair Of Lie Algebras

scholarly journals Nilpotent Lie Algebras and Systolic Growth of Nilmanifolds

2017 ◽  
Vol 2019 (9) ◽  
pp. 2763-2799
Author(s):  
Yves Cornulier
Keyword(s):  
Lie Algebras ◽  
Lie Group ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Growth Function ◽  
Nilpotent Groups ◽  
Upper Bounds ◽  
Nilpotent Lie Algebras ◽  
Open Questions ◽  
Simply Connected

Abstract Introduced by Gromov in the nineties, the systolic growth of a Lie group gives the smallest possible covolume of a lattice with a given systole. In a simply connected nilpotent Lie group, this function has polynomial growth, but can grow faster than the volume growth. We express this systolic growth function in terms of discrete cocompact subrings of the Lie algebra, making it more practical to estimate. After providing some general upper bounds, we develop methods to provide nontrivial lower bounds. We provide the first computations of the asymptotics of the systolic growth of nilpotent groups for which this is not equivalent to the volume growth. In particular, we provide an example for which the degree of growth is not an integer; it has dimension 7. Finally, we gather some open questions.

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