scholarly journals The Tamarkin–Tsygan calculus of an associative algebra à la Stasheff

2021 ◽  
Vol 23 (2) ◽  
pp. 257-282
Author(s):  
Pedro Tamaroff
Keyword(s):  
Associative Algebra ◽  
Algebra I

scholarly journals Jordan elements in a free associative algebra, I

1971 ◽  
Vol 19 (3) ◽  
pp. 354-378 ◽  
Author(s):  
David P Robbins
Keyword(s):  
Associative Algebra ◽  
Algebra I ◽  
Free Associative Algebra

Combinatorial Algebra and Its Antisymmetrized Algebra I

2015 ◽  
Vol 22 (spec01) ◽  
pp. 823-834
Author(s):  
Seul Hee Choi ◽  
Hong Goo Park ◽  
Moon-Ok Wang ◽  
Ki-Bong Nam
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Algebra I ◽  
Combinatorial Algebra

The simple non-associative algebra N(eAS, q, n, t)k and its simple subalgebras are defined in [1, 3, 5–7, 13]. In this work, we define the combinatorial algebra N(e𝔄p, n, t)k and its antisymmetrized algebra [Formula: see text] and their subalgebras. We prove that these algebras are simple. Some authors [2, 5–7, 10, 13, 14, 16, 17] found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra. We find all the derivations of the subalgebra N(e±x1x2 ⋯xn, 0, n)[1] of N(e𝔄p, n, t)k and the Lie subalgebra [Formula: see text] of [Formula: see text].

Post-quantum digital signature schemes: setting a hidden group with two-dimensional cyclicity

2020 ◽  
Vol 4 ◽  
pp. 75-82
Author(s):  
D.Yu. Guryanov ◽  
◽  
D.N. Moldovyan ◽  
A. A. Moldovyan ◽  
Keyword(s):  
Associative Algebra ◽  
Digital Signature ◽  
Quantum Signature ◽  
Commutative Group ◽  
Two Dimensional ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Fixed Element ◽  
Commutative Associative Algebra ◽  
Quantum Digital Signature

For the construction of post-quantum digital signature schemes that satisfy the strengthened criterion of resistance to quantum attacks, an algebraic carrier is proposed that allows one to define a hidden commutative group with two-dimensional cyclicity. Formulas are obtained that describe the set of elements that are permutable with a given fixed element. A post-quantum signature scheme based on the considered finite non-commutative associative algebra is described.

scholarly journals CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY

2021 ◽  
Author(s):  
MÁTYÁS DOMOKOS ◽  
VESSELIN DRENSKY
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Invariant Theory ◽  
Reductive Group ◽  
Symmetric Tensor ◽  
Free Associative Algebra ◽  
Tensor Algebra ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Degree Bounds

AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

scholarly journals On the lower central series quotients of a graded associative algebra

2011 ◽  
Vol 328 (1) ◽  
pp. 287-300 ◽  
Author(s):  
Martina Balagović ◽  
Anirudha Balasubramanian
Keyword(s):  
Associative Algebra ◽  
Lower Central Series ◽  
Central Series

Sessions of the seminar ?Algebra i Logika?

1995 ◽  
Vol 34 (1) ◽  
pp. 66-66
Keyword(s):  
Algebra I

scholarly journals Conditional expectation in an operator algebra, I

1954 ◽  
Vol 6 (2-3) ◽  
pp. 177-181 ◽  
Author(s):  
Hisaharu Umegaki
Keyword(s):  
Operator Algebra ◽  
Conditional Expectation ◽  
Algebra I
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