We review the basic notions of group theory, in particular Lie groups and Lie algebras, and of representations of the latter. Then we examine briefly their occurrence in classical physics for the description of
number theory, etc.), is very much motivated by problems in theoretical physics. For example, ...
必须承认,Pólya猜想在理论上并没有太多有趣的推论。就方法论而言,它固然是特征值估计技术的试金石,但迄今为止,在Li-Yau方法的基础上并没有本质的进步,何况几何分析学家真正感兴趣的也仅仅是第一特征值,整个higher theory还有待发展。 然而,冒着“越俎代庖”的风险,我还是想为谱几何的整体价值稍作辩护。 Laplace算...
number theory, etc.), is very much motivated by problems in theoretical physics. For example, ...
Is the FEP a Formal Theory of Semantics?representation 摘要 本文的目的有两个:(1)评估神经表征的构造在变分自由能原理及其推论过程理论、主动推理下是否发挥解释作用; (2)如果是这样,评估哪种哲学立场 相对于表征的本体论和认识论地位 是最合适的。我们专注于非现实主义(紧缩和虚构主义‑工具主义)方法...
Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements ...
Abstract Recently, Horsman et al. (Proc R Soc Lond A 470:20140182,2014) have proposed a new framework, Abstraction/Representation (AR) theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a...
Appendix B: Representation Theory of Lusztig’s Extension\mathcal LU_q This appendix is devoted to the proof of Theorem 4.6. This theorem is purely representation-theoretic in nature and is of interest in its own right. Throughoutq \in \mathbb {C}^{\times }is such thatq2is aℓth-prim...
The ability to compose new skills from a preacquired behavior repertoire is a hallmark of biological intelligence. Although artificial agents extract reusable skills from past experience and recombine them in a hierarchical manner, whether the brain simi
representation theory and cohomological - Roger, Unterberger - 1477 () Citation Context ...irasoro Lie algebra, it is highly expected that they should consequently play an important role akin to that of the Virasoro Lie algebra in two-dimensional equilibrium statistical physics (see, e.g., =-...