scholarly journals Group gradings on finite dimensional incidence algebras

2020 ◽  
Vol 544 ◽  
pp. 302-328
Author(s):  
Ednei A. Santulo ◽  
Jonathan P. Souza ◽  
Felipe Y. Yasumura
Keyword(s):  
Incidence Algebras ◽  
Finite Dimensional ◽  
Group Gradings

scholarly journals Maximal subalgebras of finite-dimensional algebras

2019 ◽  
Vol 31 (5) ◽  
pp. 1283-1304 ◽  
Author(s):  
Miodrag Cristian Iovanov ◽  
Alexander Harris Sistko
Keyword(s):  
Associative Algebra ◽  
Complete Classification ◽  
Maximal Subalgebras ◽  
Incidence Algebras ◽  
Finite Dimensional ◽  
Semisimple Algebras ◽  
Closed Fields ◽  
Representations Of Algebras ◽  
Algebraically Closed Fields ◽  
Full Classification

AbstractWe study maximal associative subalgebras of an arbitrary finite-dimensional associative algebra B over a field {\mathbb{K}} and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case and then lifting to non-semisimple algebras. The results are sharpest in the case of algebraically closed fields and take special forms for algebras presented by quivers with relations. We also relate representation theoretic properties of the algebra and its maximal and other subalgebras and provide a series of embeddings between quivers, incidence algebras and other structures which relate indecomposable representations of algebras and some subalgebras via induction/restriction functors. Some results in literature are also re-derived as a particular case, and other applications are given.

scholarly journals On H-simple not necessarily associative algebras

2019 ◽  
Vol 18 (09) ◽  
pp. 1950162
Author(s):  
A. S. Gordienko
Keyword(s):  
Associative Algebra ◽  
Hopf Algebras ◽  
Simple Algebra ◽  
Polynomial Identities ◽  
Associative Algebras ◽  
Graded Algebras ◽  
Finite Dimensional ◽  
Graded Polynomial Identities ◽  
Group Gradings ◽  
Polynomial Formula

An algebra [Formula: see text] with a generalized [Formula: see text]-action is a generalization of an [Formula: see text]-module algebra where [Formula: see text] is just an associative algebra with [Formula: see text] and a relaxed compatibility condition between the multiplication in [Formula: see text] and the [Formula: see text]-action on [Formula: see text] holds. At first glance, this notion may appear too general, however, it enables to work with algebras endowed with various kinds of additional structures (e.g. comodule algebras over Hopf algebras, graded algebras, algebras with an action of a semigroup by anti-endomorphisms). This approach proves to be especially fruitful in the theory of polynomial identities. We show that if [Formula: see text] is a finite dimensional (not necessarily associative) algebra over a field of characteristic [Formula: see text] and [Formula: see text] is simple with respect to a generalized [Formula: see text]-action, then there exists [Formula: see text] where [Formula: see text] is the sequence of codimensions of polynomial [Formula: see text]-identities of [Formula: see text]. In particular, if [Formula: see text] is a finite dimensional (not necessarily group graded) graded-simple algebra, then there exists [Formula: see text] where [Formula: see text] is the sequence of codimensions of graded polynomial identities of [Formula: see text]. In addition, we study the free-forgetful adjunctions corresponding to (not necessarily group) gradings and generalized [Formula: see text]-actions.

scholarly journals Graded-division algebras over arbitrary fields

2020 ◽  
pp. 2140009
Author(s):  
Yuri Bahturin ◽  
Alberto Elduque ◽  
Mikhail Kochetov
Keyword(s):  
Finite Groups ◽  
Closed Field ◽  
Arbitrary Field ◽  
Division Algebras ◽  
Real Numbers ◽  
Arbitrary Group ◽  
Matrix Algebras ◽  
Finite Dimensional ◽  
Group Gradings

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a classification of finite-dimensional graded-central graded-division algebras over an arbitrary field [Formula: see text] can be reduced to the following three classifications, for each finite Galois extension [Formula: see text] of [Formula: see text]: (1) finite-dimensional central division algebras over [Formula: see text], up to isomorphism; (2) twisted group algebras of finite groups over [Formula: see text], up to graded-isomorphism; (3) [Formula: see text]-forms of certain graded matrix algebras with coefficients in [Formula: see text] where [Formula: see text] is as in (1) and [Formula: see text] is as in (2). As an application, we classify, up to graded-isomorphism, the finite-dimensional graded-division algebras over the field of real numbers (or any real closed field) with an abelian grading group. We also discuss group gradings on fields.

scholarly journals Group Gradings on Finite Dimensional Lie Algebras

2013 ◽  
Vol 20 (04) ◽  
pp. 573-578 ◽  
Author(s):  
Dušan Pagon ◽  
Dušan Repovš ◽  
Mikhail Zaicev
Keyword(s):  
Finite Group ◽  
Lie Algebras ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Solvable Radical ◽  
Finite Dimensional ◽  
Levi Subalgebra ◽  
Group Gradings ◽  
Finite Dimensional Lie Algebras

We study gradings by non-commutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if L is graded by a non-abelian finite group G, then the solvable radical R of L is G-graded and there exists a Levi subalgebra B=H1⊕ ⋯ ⊕ Hm homogeneous in G-grading with graded simple summands H1,…,Hm. All Supp Hi (i=1,…,m) are commutative subsets of G.

Group Gradings in Incidence Algebras

2010 ◽  
Vol 38 (3) ◽  
pp. 953-963 ◽  
Author(s):  
Lance Miller ◽  
Eugene Spiegel
Keyword(s):  
Incidence Algebras ◽  
Group Gradings

Group Gradings on Associative Algebras with Involution

2008 ◽  
Vol 51 (2) ◽  
pp. 182-194 ◽  
Author(s):  
Y. A. Bahturin ◽  
A. Giambruno
Keyword(s):  
Abelian Group ◽  
Matrix Algebra ◽  
Finite Abelian Group ◽  
Closed Field ◽  
Base Field ◽  
Associative Algebras ◽  
Finite Dimensional ◽  
The Matrix ◽  
Simple Algebras ◽  
Group Gradings

AbstractIn this paper we describe the group gradings by a finite abelian group G of the matrix algebra Mn(F) over an algebraically closed field F of characteristic different from 2, which respect an involution (involution gradings). We also describe, under somewhat heavier restrictions on the base field, all G-gradings on all finite-dimensional involution simple algebras.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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