Non-commutative Poisson Algebras Admitting a Multiplicative Basis

2020 ◽  
pp. 103-112
Author(s):  
Antonio J. Calderón Martín ◽  
Boubacar Dieme ◽  
Francisco J. Navarro Izquierdo
Keyword(s):  
Poisson Algebras ◽  
Multiplicative Basis

Regular Hom-algebras admitting a multiplicative basis

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonio J. Calderón Martín
Keyword(s):  
Arbitrary Dimension ◽  
Base Field ◽  
Direct Sum ◽  
Multiplicative Basis ◽  
Arbitrary Base ◽  
The Family

AbstractLet {({\mathfrak{H}},\mu,\alpha)} be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field {{\mathbb{F}}}. A basis {{\mathcal{B}}=\{e_{i}\}_{i\in I}} of {{\mathfrak{H}}} is called multiplicative if for any {i,j\in I}, we have that {\mu(e_{i},e_{j})\in{\mathbb{F}}e_{k}} and {\alpha(e_{i})\in{\mathbb{F}}e_{p}} for some {k,p\in I}. We show that if {{\mathfrak{H}}} admits a multiplicative basis, then it decomposes as the direct sum {{\mathfrak{H}}=\bigoplus_{r}{{\mathfrak{I}}}_{r}} of well-described ideals admitting each one a multiplicative basis. Also, the minimality of {{\mathfrak{H}}} is characterized in terms of the multiplicative basis and it is shown that, in case {{\mathcal{B}}}, in addition, it is a basis of division, then the above direct sum is composed by means of the family of its minimal ideals, each one admitting a multiplicative basis of division.

scholarly journals Poisson algebras via model theory and differential-algebraic geometry

2017 ◽  
Vol 19 (7) ◽  
pp. 2019-2049 ◽  
Author(s):  
Jason Bell ◽  
Stéphane Launois ◽  
Omar León Sánchez ◽  
Rahim Moosa
Keyword(s):  
Algebraic Geometry ◽  
Model Theory ◽  
Poisson Algebras

Proper T-ideals of poisson algebras with extreme properties

2016 ◽  
Vol 71 (6) ◽  
pp. 224-232
Author(s):  
S. M. Ratseev
Keyword(s):  
Poisson Algebras

Kähler–Poisson algebras

2019 ◽  
Vol 136 ◽  
pp. 156-172 ◽  
Author(s):  
Joakim Arnlind ◽  
Ahmed Al-Shujary
Keyword(s):  
Poisson Algebras

scholarly journals Nambu–Poisson bracket on superspace

2018 ◽  
Vol 15 (11) ◽  
pp. 1850190 ◽  
Author(s):  
Viktor Abramov
Keyword(s):  
Poisson Bracket ◽  
Jacobi Identity ◽  
Leibniz Rule ◽  
Smooth Functions ◽  
Poisson Algebras ◽  
Fundamental Identity ◽  
Odd Degree ◽  
New Formula ◽  
Usual Formula

We propose an extension of [Formula: see text]-ary Nambu–Poisson bracket to superspace [Formula: see text] and construct by means of superdeterminant a family of Nambu–Poisson algebras of even degree functions, where the parameter of this family is an invertible transformation of Grassmann coordinates in superspace [Formula: see text]. We prove in the case of the superspaces [Formula: see text] and [Formula: see text] that our [Formula: see text]-ary bracket, defined with the help of superdeterminant, satisfies the conditions for [Formula: see text]-ary Nambu–Poisson bracket, i.e. it is totally skew-symmetric and it satisfies the Leibniz rule and the Filippov–Jacobi identity (fundamental identity). We study the structure of [Formula: see text]-ary bracket defined with the help of superdeterminant in the case of superspace [Formula: see text] and show that it is the sum of usual [Formula: see text]-ary Nambu–Poisson bracket and a new [Formula: see text]-ary bracket, which we call [Formula: see text]-bracket, where [Formula: see text] is the product of two odd degree smooth functions.

scholarly journals Kähler-Poisson Algebras

2020 ◽  
Author(s):  
Ahmed Al-Shujary
Keyword(s):  
Poisson Algebras

The Structure of Poisson Algebras

1985 ◽  
Vol 2 (1) ◽  
pp. 69-73 ◽  
Author(s):  
G. A. RlNGWOOD
Keyword(s):  
Poisson Algebras
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