scholarly journals ExteriorModules: a package for computing monomial modules over an exterior algebra

2021 ◽  
Vol 11 (1) ◽  
pp. 71-81
Author(s):  
Luca Amata ◽  
Marilena Crupi
Keyword(s):  
Exterior Algebra

scholarly journals Integral calculus on quantum exterior algebras

2014 ◽  
Vol 11 (04) ◽  
pp. 1450026 ◽  
Author(s):  
Serkan Karaçuha ◽  
Christian Lomp
Keyword(s):  
Differential Calculus ◽  
Polynomial Algebra ◽  
Exterior Algebra ◽  
Integral Calculus ◽  
De Rham Complex ◽  
Integral Forms ◽  
Rham Complex ◽  
De Rham ◽  
Quantum Polynomial

Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

Exterior algebra

1967 ◽  
pp. 95-140
Author(s):  
W. H. Greub
Keyword(s):  
Exterior Algebra

Multi-particle Spaces

2020 ◽  
pp. 187-200
Author(s):  
Daniel Canarutto
Keyword(s):  
Operator Algebra ◽  
Particle Physics ◽  
Arbitrary Number ◽  
Exterior Algebra ◽  
Linear Combinations ◽  
Absorption And Emission ◽  
Dirac Type ◽  
Natural Generalisation ◽  
Finite Linear ◽  
Number Of Particles

The fundamental algebraic notions needed in many-particle physics are exposed. Spaces of free states containing an arbitrary number of particles of many types are introduced. The operator algebra generated by absorption and emission operators is studied as a natural generalisation of standard exterior algebra. The link between the discrete and the distributional formalisms is provided by the spaces of finite linear combinations of semi-densities of Dirac type.

Complete Decomposability in the Exterior Algebra of a Free Module

1980 ◽  
Vol 32 (1) ◽  
pp. 27-33 ◽  
Author(s):  
M. Boratynski ◽  
E. D. Davis ◽  
A. V. Geramita
Keyword(s):  
Commutative Ring ◽  
Present Note ◽  
Free Module ◽  
Exterior Algebra ◽  
Standard Bases ◽  
Classical Criterion ◽  
Generally True

Recall the classical criterion for the complete decomposability of exterior vectors: the completely decomposable vectors in ∧pRn, R a field, are precisely the “Plücker vectors,” i.e. those whose coordinates (relative to the standard bases for ∧pRn) satisfy the Plücker equations. For R an arbitrary commutative ring, completely decomposable exterior vectors are still Plücker vectors, but the converse is not generally true. Rings for which the converse is true (for all 1 ≤ p ≤ n) are called Towber rings. Noetherian Towber rings are regular and, in fact, are characterized by the property that every Plücker vector in ∧2R4 is completely decomposable. (See [10] for these two results as well as for the above mentioned facts.) The present note develops a new characterization of Towber rings, combining it with results of Kleiner [9] and Estes-Matijevic [5] in (1) below.

scholarly journals Twisted Dickson–Mui invariants and the Steinberg module multiplicity

2011 ◽  
Vol 151 (1) ◽  
pp. 43-57 ◽  
Author(s):  
JINKUI WAN ◽  
WEIQIANG WANG
Keyword(s):  
Tensor Product ◽  
Linear Group ◽  
General Linear Group ◽  
Exterior Algebra ◽  
Symmetric Algebra ◽  
General Linear ◽  
Parabolic Subgroups ◽  
Steinberg Module ◽  
Finite General Linear Group

AbstractWe determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S•(V) and the exterior algebra ∧•(V) of the natural GLn(q)-module V. In addition, we obtain the graded multiplicity of the Steinberg module of GLn(q) in S•(V) ⊗ ∧•(V), twisted by an arbitrary determinant power.

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