Suman Rani | Searcharxiv

arXiv2026

Automorphism groups and derivation algebras of Hamiltonian Lie algebras

In this paper, we compute the automorphism group and derivation algebra of the Hamiltonian Lie algebra $\mathcal{H}_{N}$ and its derived subalgebra $\mathcal{H}_{N}'$, where $N$ is an even positive integer. The automorphism groups are shown to be $\mathbf{GSp}_{N}(\mathbb{Z})\ltimes (\mathbb{\mathbb{K}}^{\times})^{N}$ for both Lie algebras and we prove that all derivations are inner for the Hamiltonian Lie algebra, also we compute the full derivation space for the derived subalgebra of Hamiltonian Lie algebra. Finally we compute the second cohomology group of Hamiltonian Lie algebra.

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arXiv2026

Integrable Representations for Toroidal Lie Algebras Co-ordinated by Rational Quantum Torus

We classify irreducible integrable modules with finite-dimensional weight spaces for toroidal Lie algebras coordinated by rational quantum torus with trivial central action. Let $\mathbb{C}_q$ denote the rational quantum torus associated with a rational quantum matrix $q$, and let $\hat{\tau}(d,q)$ be the toroidal Lie algebra coordinated by rational quantum torus obtained by adjoining the derivation space $D$ to the universal central extension $\tilde{\tau}(d,q)=\mathfrak{sl}_d(\mathbb{C}_q)\oplus HC_1(\mathbb{C}_q)$ of $\mathfrak{sl}_d(\mathbb{C}_q)$. The case of nontrivial central action was previously classified by S. Eswara Rao and K. Zhao. The present work completes the classification by describing all irreducible integrable $\hat{\tau}(d,q)$-modules with finite-dimensional weight spaces in the case where the $n$-dimensional center $C$ acts trivially on the modules.

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