scholarly journals A wild automorphism of a free Novikov algebra

2018 ◽  
Vol 15 ◽  
pp. 1671-1679 ◽  
Author(s):  
B. A. Duisengaliyeva ◽  
U. U. Umirbaev
Keyword(s):  
Novikov Algebra ◽  
Wild Automorphism

scholarly journals Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras

2017 ◽  
Vol 16 (01) ◽  
pp. 1750001 ◽  
Author(s):  
L. A. Bokut ◽  
Yuqun Chen ◽  
Zerui Zhang
Keyword(s):  
Word Problem ◽  
Type Theorem ◽  
Novikov Algebra ◽  
Base Theory ◽  
Novikov Algebras

We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.

scholarly journals Flag manifolds and the Landweber–Novikov algebra

1998 ◽  
Vol 2 (1) ◽  
pp. 79-101 ◽  
Author(s):  
Victor M Buchstaber ◽  
Nigel Ray
Keyword(s):  
Flag Manifolds ◽  
Novikov Algebra

Krichever-Novikov Algebra, supersymmetrization

2004 ◽  
pp. 224-224
Author(s):  
Maurice Kibler ◽  
Mohammed Daoud ◽  
Maurice Kibler ◽  
I. Carrillo-Ibarra ◽  
Hugo Garcia-Compean ◽  
...  
Keyword(s):  
Novikov Algebra

scholarly journals On the Solvability of ℤ3-Graded Novikov Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 312
Author(s):  
Viktor Zhelyabin ◽  
Ualbai Umirbaev
Keyword(s):  
Finite Order ◽  
Algebraic Systems ◽  
Novikov Algebra ◽  
Novikov Algebras

Symmetries of algebraic systems are called automorphisms. An algebra admits an automorphism of finite order n if and only if it admits a Zn-grading. Let N=N0⊕N1⊕N2 be a Z3-graded Novikov algebra. The main goal of the paper is to prove that over a field of characteristic not equal to 3, the algebra N is solvable if N0 is solvable. We also show that a Z2-graded Novikov algebra N=N0⊕N1 over a field of characteristic not equal to 2 is solvable if N0 is solvable. This implies that for every n of the form n=2k3l, any Zn-graded Novikov algebra N over a field of characteristic not equal to 2,3 is solvable if N0 is solvable.

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