TY - JOUR
T1 - Non-associative structures of commutative algebras related with quadratic Poisson brackets
AU - Artemovych, Orest D.
AU - Blackmore, Denis
AU - Prykarpatski, Anatolij K.
N1 - Publisher Copyright:
© 2020, The Author(s).
PY - 2020/3/1
Y1 - 2020/3/1
N2 - There are studied algebraic properties of quadratic Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Their relations both with derivations of symmetric tensor algebras and Yang–Baxter structures on the adjacent Lie algebras are demonstrated. Special attention is paid to quadratic Poisson brackets of Lie–Poisson type, examples of Balinsky–Novikov and Leibniz algebras are discussed. The non-associative structures of commutative algebras related with Balinsky–Novikov, Leibniz, Lie, and Zinbiel algebras are studied in detail.
AB - There are studied algebraic properties of quadratic Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Their relations both with derivations of symmetric tensor algebras and Yang–Baxter structures on the adjacent Lie algebras are demonstrated. Special attention is paid to quadratic Poisson brackets of Lie–Poisson type, examples of Balinsky–Novikov and Leibniz algebras are discussed. The non-associative structures of commutative algebras related with Balinsky–Novikov, Leibniz, Lie, and Zinbiel algebras are studied in detail.
KW - Balinsky–Novikov algebra
KW - Derivation
KW - Leibniz algebra
KW - Lie algebra
KW - Lie–Poisson structure
KW - Pre-Poisson brackets
KW - Zinbiel algebra
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U2 - 10.1007/s40879-020-00398-w
DO - 10.1007/s40879-020-00398-w
M3 - Article
AN - SCOPUS:85079436164
SN - 2199-675X
VL - 6
SP - 208
EP - 231
JO - European Journal of Mathematics
JF - European Journal of Mathematics
IS - 1
ER -