Št. zadetkov: 16
Izvirni znanstveni članek
Oznake:
polynomial identities;graded algebras;codimensions;exponential growth;
We study polynomial identities of nonassociative algebras constructed by using infinite binary words and their combinatorial properties. Infinite periodic and Sturmian words were first applied for constructing examples of algebras with an arbitrary real PI-exponent greater than one. Later, we used t ...
Leto:
2018
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
polynomial identities;graded algebras;codimensions;exponential growth;
We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid ▫$\Gamma$▫. First, we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra ▫$A$▫, we prove the existence of the graded PI-exponent, provi ...
Leto:
2017
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
polynomial identities;Lie superalgebras;graded algebras;codimensions;exponential growth;Pauli gradings;
We introduce grading on certain finite dimensional simple Lie superalgebras of type ▫$P(t)$▫ by elementary abelian 2-group. This grading gives rise to Pauli matrices and is a far generalization of ▫$(\mathbb{Z}_2 \times \mathbb{Z}_2)$▫-grading on Lie algebra of ▫$(2 \times 2)$▫-traceless matrices.We ...
Leto:
2017
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
left nilpotent algebra;polynomial identity;codimension;subexponential function of combinatorial complexity;PI-exponent;
Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with specified properties of the codimension sequence. However, the class ...
Leto:
2019
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
codimension;exponential growth;fractional PI-exponent;non-associative unital algebra;polynomial identity;
We study polynomial identities of algebras with adjoined external unit. For a wide class of algebras we prove that adjoining external unit element leads to increasing of PI-exponent precisely to 1. We also show that any real number from the interval ▫$[2,3]$▫ can be realized as PI-exponent of some u ...
Leto:
2015
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
graded polynomial identities;Lie superalgebras;codimensions;exponential growth;PI-exponent;
We study asymptotic behaviour of graded codimensions of Lie superalgebra ▫$b(2)$▫. We prove that graded PI-exponent exists and is equal to $3 + 2\sqrt 3$.
Leto:
2015
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
graded polynomial identities;Lie superalgebras;codimensions;PI-exponent;
We study ▫$\mathbb{Z}_2$▫-graded identities of simple Lie superalgebras over a field of characteristic zero. We prove the existence of the graded PI-exponent for such algebras.
Leto:
2016
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
matematika;identitete;kodimenzija;eksponentna rast;
The asymptotic behaviour is studied of exponentially bounded sequences of codimensions of identities of algebras with unity. A series of algebras is constructed for which the base of the exponential increases by exactly 1 when an outer unity is adjoined to the original algebra. It is shown that the ...
Leto:
2015
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
polynomial identities;Lie superalgebras;graded identities;codimensions;exponential growth;
We study numerical invariants of identities of finite-dimensional solvable Lie superalgebras. We define new series of finite-dimensional solvable Lie superalgebras L with non-nilpotent derived subalgebra ▫$L'$▫ and discuss their codimension growth. For the first algebra of this series we prove the e ...
Leto:
2018
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Kratki znanstveni prispevek
Oznake:
We consider polynomial identities and codimension growth of nonassociative algebras over a field of characte-ristics zero. We offer new approach which allows to construct nonassociative algebras starting from a given infinite binary word. The sequence of codimensions of such an algebra is closeely c ...
Leto:
2019
Vir:
Fakulteta za matematiko in fiziko (UL FMF)