An algorithm for recognising the exterior square of a matrix

1999 ◽  
Vol 46 (3) ◽  
pp. 213-244 ◽  
Author(s):  
Catherine Greenhill
Keyword(s):  
Exterior Square

scholarly journals An Algorithm for Recognising the Exterior Square of a Multiset

2000 ◽  
Vol 3 ◽  
pp. 96-116 ◽  
Author(s):  
Catherine Greenhill
Keyword(s):  
Abelian Group ◽  
Vector Space ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Combinatorial Construction ◽  
Exterior Square

AbstractThe exterior square of a multiset is a natural combinatorial construction which is related to the exterior square of a vector space. We consider multisets of elements of an abelian group. Two properties are defined which a multiset may satisfy: recognisability and involution-recognisability. A polynomial-time algorithm is described which takes an input multiset and returns either (a) a multiset which is either recognisable or involution-recognisable and whose exterior square equals the input multiset, or (b) the message that no such multiset exists. The proportion of multisets which are neither recognisable nor involution-recognisable is shown to be small when the abelian group is finite but large. Some further comments are made about the motivating case of multisets of eigenvalues of matrices.

scholarly journals The Schur multiplier of groups of order 𝑝5

2019 ◽  
Vol 22 (4) ◽  
pp. 647-687 ◽  
Author(s):  
Sumana Hatui ◽  
Vipul Kakkar ◽  
Manoj K. Yadav
Keyword(s):  
Schur Multiplier ◽  
Tensor Square ◽  
Exterior Square

AbstractIn this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian p-groups of order {p^{5}}. As an application, we determine the capability of groups of order {p^{5}}.

scholarly journals On the non-abelian tensor square of all groups of order dividing p5

2020 ◽  
pp. 2150107
Author(s):  
Taleea Jalaeeyan Ghorbanzadeh ◽  
Mohsen Parvizi ◽  
Peyman Niroomand
Keyword(s):  
Homotopy Group ◽  
The Third ◽  
Tensor Square ◽  
Exterior Square

In this paper, we consider all groups of order dividing [Formula: see text]. We obtain the explicit structure of the non-abelian tensor square, non-abelian exterior square, tensor center, exterior center, the third homotopy group of suspension of an Eilenberg–MacLane space [Formula: see text] and [Formula: see text] of such groups.

scholarly journals Certain functors of nilpotent Lie algebras with the derived subalgebra of dimension two

2019 ◽  
Vol 19 (01) ◽  
pp. 2050012
Author(s):  
Farangis Johari ◽  
Peyman Niroomand
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Schur Multiplier ◽  
Nilpotent Lie Algebra ◽  
Nilpotent Lie Algebras ◽  
Dimension Formula ◽  
Tensor Square ◽  
Exterior Square

By considering the nilpotent Lie algebra with the derived subalgebra of dimension [Formula: see text], we compute some functors including the Schur multiplier, the exterior square and the tensor square of these Lie algebras. We also give the corank of such Lie algebras.

scholarly journals THE SECOND QUANDLE HOMOLOGY OF THE TAKASAKI QUANDLE OF AN ODD ABELIAN GROUP IS AN EXTERIOR SQUARE OF THE GROUP

2011 ◽  
Vol 20 (01) ◽  
pp. 171-177 ◽  
Author(s):  
MACIEJ NIEBRZYDOWSKI ◽  
JÓZEF H. PRZYTYCKI
Keyword(s):  
Abelian Group ◽  
Exterior Product ◽  
Link Invariants ◽  
Fundamental Step ◽  
Odd Order ◽  
Exterior Square

We prove that if G is an abelian group of odd order then there is an isomorphism from the second quandle homology [Formula: see text] to G ∧ G, where ∧ is the exterior product. In particular, for [Formula: see text], k odd, we have [Formula: see text]. Nontrivial [Formula: see text] allows us to use 2-cocycles to construct new quandles from T(G), and to construct link invariants. Computation of [Formula: see text] is also the first, fundamental step in the direction of computing homology of Takasaki quandles in general.

scholarly journals LOCAL NEWFORMS AND FORMAL EXTERIOR SQUARE L-FUNCTIONS

2013 ◽  
Vol 09 (08) ◽  
pp. 1995-2010 ◽  
Author(s):  
MICHITAKA MIYAUCHI ◽  
TAKUYA YAMAUCHI
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Principal Series ◽  
Whittaker Function ◽  
Series Representations ◽  
Principal Series Representations ◽  
Exterior Square

Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GL n(F). In this paper, we show that the Jacquet–Shalika integral attains a certain L-function, the so-called formal exterior square L-function, when the Whittaker function is associated to a newform for π. By considerations on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations.

scholarly journals Non-exterior square graph of finite group

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 877-883
Author(s):  
P. Niroomand ◽  
A. Erfanian ◽  
M. Parvizi ◽  
B. Tolue
Keyword(s):  
Finite Group ◽  
Group Structure ◽  
Vertex Set ◽  
Square Graph ◽  
Exterior Square

We define the non-exterior square graph ??G which is a graph associated to a non-cyclic finite group with the vertex set G\?Z(G), where ?Z(G) denotes the exterior centre of G, and two vertices x and y are joined whenever x ^ y ? 1, where ^ denotes the operator of non-abelian exterior square. In this paper, we investigate how the group structure can be affected by the planarity, completeness and regularity of this graph.

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