Almost primitive elements of free nonassociative (anty)commutative algebras of small rank

2012 ◽  
Vol 67 (5-6) ◽  
pp. 206-210 ◽  
Author(s):  
A. V. Klimakov
Keyword(s):  
Primitive Elements ◽  
Small Rank ◽  
Commutative Algebras

scholarly journals NON-SYMPLECTIC INVOLUTIONS ON MANIFOLDS OF -TYPE

2020 ◽  
pp. 1-25
Author(s):  
CHIARA CAMERE ◽  
ALBERTO CATTANEO ◽  
ANDREA CATTANEO
Keyword(s):  
Moduli Spaces ◽  
Quadratic Forms ◽  
Symplectic Manifolds ◽  
Hilbert Schemes ◽  
Small Rank ◽  
Twisted Sheaves ◽  
Formula Type

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all $d$ -dimensional families of manifolds of $K3^{[n]}$ -type with a non-symplectic involution for $d\geqslant 19$ and $n\leqslant 5$ and provide examples arising as moduli spaces of twisted sheaves on a $K3$ surface.

scholarly journals Serre–Swan theorem for non-commutative -algebras

2003 ◽  
Vol 48 (2-3) ◽  
pp. 275-296 ◽  
Author(s):  
Katsunori Kawamura
Keyword(s):  
Commutative Algebras

scholarly journals The Homological Kähler-de Rham Differential Mechanism: II. Sheaf-Theoretic Localization of Quantum Dynamics

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Anastasios Mallios ◽  
Elias Zafiris
Keyword(s):  
Quantum Dynamics ◽  
Dynamical Behavior ◽  
Quantum Regime ◽  
Commutative Algebras ◽  
Differential Mechanism ◽  
De Rham ◽  
Physical Fields

The homological Kähler-de Rham differential mechanism models the dynamical behavior of physical fields by purely algebraic means and independently of any background manifold substratum. This is of particular importance for the formulation of dynamics in the quantum regime, where the adherence to such a fixed substratum is problematic. In this context, we show that the functorial formulation of the Kähler-de Rham differential mechanism in categories of sheaves of commutative algebras, instantiating generalized localization environments of physical observables, induces a consistent functorial framework of dynamics in the quantum regime.

scholarly journals Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category

Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Laurent Poinsot
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Semidirect Product ◽  
Hopf Algebras ◽  
Formal Series ◽  
Product Structure ◽  
Locally Finite ◽  
Commutative Algebras ◽  
Affine Groups ◽  
Formal Power

A locally finite category is defined as a category in which every arrow admits only finitely many different ways to be factorized by composable arrows. The large algebra of such categories over some fields may be defined, and with it a group of invertible series (under multiplication). For certain particular locally finite categories, a substitution operation, generalizing the usual substitution of formal power series, may be defined, and with it a group of reversible series (invertible under substitution). Moreover, both groups are actually affine groups. In this contribution, we introduce their coordinate Hopf algebras which are both free as commutative algebras. The semidirect product structure obtained from the action of reversible series on invertible series by anti-automorphisms gives rise to an interaction at the level of their coordinate Hopf algebras under the form of a smash coproduct.

THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE

2009 ◽  
Vol 19 (01) ◽  
pp. 117-133 ◽  
Author(s):  
MATEJ MENCINGER ◽  
MILAN KUTNJAK
Keyword(s):  
Algebraic Approach ◽  
Dynamical Analysis ◽  
Algebraic Classification ◽  
Commutative Algebras ◽  
Planar Maps ◽  
Points Of View ◽  
One To One

The dynamics of discrete homogeneous quadratic planar maps is considered via the algebraic approach. There is a one-to-one correspondence between these systems and 2D commutative algebras (c.f. [Markus, 1960]). In particular, we consider the systems corresponding to algebras which contain some nilpotents of rank two (i.e. NQ-systems). Markus algebraic classification is used to obtain the class representatives. The case-by-case dynamical analysis is presented. It is proven that there is no chaos in NQ-systems. Yet, some cases are really interesting from the dynamical and bifurcational points of view.

Automorphisms with centralizers of small rank

2010 ◽  
pp. 564-585 ◽  
Author(s):  
Evgeny Khukhro ◽  
Victor Mazurov
Keyword(s):  
Small Rank
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