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Bar-invariant bases of the quantum cluster algebra of type $A_{2}^{(2)}$

Xueqing Chen; Ming Ding; Jie Sheng — 2011

Czechoslovak Mathematical Journal

We construct bar-invariant $ℤ [q^{\pm 1 / 2}]$ -bases of the quantum cluster algebra of the valued quiver $A_{2}^{(2)}$ , one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947–974.

Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms

Zhiqi Chen; Xueqing Chen; Ming Ding — 2020

Czechoslovak Mathematical Journal

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian superoperator in a supervariable. In this paper, we show that fermionic Novikov algebras equipped with invariant non-degenerate symmetric bilinear forms are Novikov algebras.

On the classification of $3$ -dimensional $F$ -manifold algebras

Zhiqi Chen; Jifu Li; Ming Ding — 2022

Czechoslovak Mathematical Journal

$F$ -manifold algebras are focused on the algebraic properties of the tangent sheaf of $F$ -manifolds. The local classification of 3-dimensional $F$ -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional $F$ -manifold algebras over the complex field $ℂ$ .

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Currently displaying 1 – 3 of 3

Bar-invariant bases of the quantum cluster algebra of type $A_{2}^{(2)}$

Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms

On the classification of $3$ -dimensional $F$ -manifold algebras

Advanced Search

Formula preview

Currently displaying 1 – 3 of 3

Bar-invariant bases of the quantum cluster algebra of type A 2 ( 2 )

Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms

On the classification of 3 -dimensional F -manifold algebras

Bar-invariant bases of the quantum cluster algebra of type $A_{2}^{(2)}$

On the classification of $3$ -dimensional $F$ -manifold algebras