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pro vyhledávání: '"Murray, Scott A"'
This study extends previous research on spatial representations in multimodal AI systems. Although current models demonstrate a rich understanding of spatial information from images, this information is rooted in propositional representations, which
Externí odkaz:
http://arxiv.org/abs/2409.13929
Let $G(\mathbb{Q})$ be a simply connected Chevalley group over $\mathbb{Q}$ corresponding to a simple Lie algebra $\mathfrak g$ over $\mathbb{C}$. Let $V$ be a finite dimensional faithful highest weight $\mathfrak g$-module and let $V_\mathbb{Z}$ be
Externí odkaz:
http://arxiv.org/abs/2408.16895
Let $\mathfrak{g}$ be a symmetrizable Kac--Moody algebra. Given a root $\alpha$ and a real root $\beta$ of $\mathfrak{g}$, it is known that the $\beta$-string through $\alpha$, denoted $R_\alpha(\beta)$, is finite. Given an imaginary root $\beta$, we
Externí odkaz:
http://arxiv.org/abs/2403.01687
The Monster Lie algebra $\frak m $, which admits an action of the Monster finite simple group $\mathbb{M}$, was introduced by Borcherds as part of his work on the Conway--Norton Monstrous Moonshine conjecture. Here we construct an analog~$G(\frak m)$
Externí odkaz:
http://arxiv.org/abs/2311.11078
The Monster Lie algebra $\mathfrak m$ is a quotient of the physical space of the vertex algebra $V=V^\natural\otimes V_{1,1}$, where $V^\natural$ is the Moonshine module vertex operator algebra of Frenkel, Lepowsky, and Meurman, and $V_{1,1}$ is the
Externí odkaz:
http://arxiv.org/abs/2210.16178
Let $A$ be a symmetrizable generalized Cartan matrix with corresponding Kac--Moody algebra $\frak{g}$ over ${\mathbb Q}$. Let $V=V^{\lambda}$ be an integrable highest weight $\frak{g}$-module and let $V_{\mathbb Z}=V^{\lambda}_{\mathbb Z}$ be a ${\ma
Externí odkaz:
http://arxiv.org/abs/2210.01644
Publikováno v:
In iScience 16 August 2024 27(8)
Publikováno v:
In Journal of Pure and Applied Algebra July 2024 228(7)
Publikováno v:
In Journal of Financial Economics March 2024 153
We describe various approaches to constructing groups which may serve as Lie group analogs for the monster Lie algebra of Borcherds.
Comment: To appear in Letters in Math. Phys
Comment: To appear in Letters in Math. Phys
Externí odkaz:
http://arxiv.org/abs/2002.06658