Local GL(d,R) Lie group for solving quantum ADM constraints

Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groups

Quantum mechanical systems with position dependent masses (PDM) admitting for and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a three parametric Lie group, admit at least one second order integral of motion. The presented classification is partially extended to the more generic systems which admit one or two parametric Lie groups.

Application of the admitted Lie group of the \\ classical Boltzmann equation to classification of the \\ Boltzmann equation with a source term

The classical Boltzmann equation is an integro-differential equation which describes the time evolution of rarefied gas in terms of a molecular distribution function. For some kinetic problems where it is necessary to add in the Boltzmann equation a source term depending on the independent and dependent variables. This paper is devoted to applying preliminary group classification to the Boltzmann equation with a source function by using the Lie group $L_{11}$ admitted by the classical Boltzmann equation. The developed strategy for deriving determining equation of an integro-differential equati…

耗散复杂性的几何：通过李楔与不变锥实现马尔可夫量子动力学的类莱维分解定理

The Geometry of Dissipative Complexity: A Levi-Type Decomposition Theorem for Markovian Quantum Dynamics via Lie Wedges and Invariant Cones

本研究针对马尔可夫量子动力学的动力学李楔，证明了类莱维分解与重构定理，揭示了耗散在生成元几何中的编码方式，拓展了李代数结构方法至不可逆马尔可夫控制领域。

用于求解Lévy-Leblond方程的分次色李超代数

Graded colour Lie superalgebras for solving Lévy-Leblond equations

本文通过研究时间无关的Lévy-Leblond方程，构造了更高分次的色李超代数，并将其应用于自由方程求解和谐振子谱的计算。

具有依赖于位置的质量且关于双参数李群不变的超可积量子力学系统

Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups

本研究分类了具有位置依赖质量且容许双参数李对称群、至少含一个二阶运动积分的量子力学系统，并将该分类部分推广到无李群的更一般系统。

Nets of standard subspaces induced by antiunitary representations of admissible Lie groups I

Let $(π, \mathcal{H})$ be a strongly continuous unitary representation of a 1-connected Lie group $G$ such that the Lie algebra $\mathfrak{g}$ of $G$ is generated by the positive cone $C_π:= \{x \in \mathfrak{g} : -i\partial π(x) \geq 0\}$ and an element $h$ for which the adjoint representation of $h$ induces a 3-grading of $\mathfrak{g}$. Moreover, suppose that $(π, \mathcal{H})$ extends to an antiunitary representation of the extended Lie group $G_τ:= G \rtimes \{\mathbf{1}, τ_G\}$, where $τ_G$ is an involutive automorphism of $G$ with $\mathbf{L}(τ_G) = e^{iπ\mathrm{ad} h}$. In a recent wor…