Related papers: Segal's Gamma rings and universal arithmetic

In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as a subalgebra of the ring of invariants of a certain noncommutative ring with respect to the action of $S_1\times S_2\times\cdots\times S_n$, where $S_j$ is…

Let $K$ be a field, $\Gamma $ a finite group of field automorphisms of $K$, $F$ the $\Gamma $-fixed field in $K$ and $G\leq $GL$_v(K)$ a finite matrix group. Then the action of $\Gamma $ defines a grading on the symmetric algebra of the…

In a previous paper Cuntz and Deninger introduced the ring $C(R)$ for a perfect $\mathbb{F}_p$-algebra $R$. The ring $C(R)$ is canonically isomorphic to the $p$-typical Witt ring $W(R)$. In fact there exist canonical isomorphisms $\alpha_n…

Let $\mathfrak{g}$ be a simply laced Lie algebra, $\widehat{\mathfrak{g}}_1$ the corresponding affine Lie algebra at level one, and $\mathcal{W}(\mathfrak{g})$ the corresponding Casimir W-algebra. We consider…

We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector…

We show that for the reductive Tannaka groups of semisimple holonomic $\mathscr{D}$-modules on abelian varieties, every Weyl group orbit of weights of their universal cover is realized by a conic Lagrangian cycle on the cotangent bundle.…

The classical Witt vectors are a ubiquitous object in algebra and number theory. They arise as a functorial construction that takes perfect fields k of prime characteristic p > 0 to p-adically complete discrete valuation rings of…

Based on our previous work on an arithmetic analogue of Christol's theorem, this paper studies in more detail the structure of the lambda-ring $E_K = K \otimes W_{O_K}^a (O_{\bar{K}})$ of algebraic Witt vectors for number fields $K$. First…

In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical…

We associate to an arbitrary positive root $\alpha$ of a complex semisimple finite-dimensional Lie algebra $\mfrak{g}$ a twisting endofunctor $T_\alpha$ of the category of $\mfrak{g}$-modules. We apply this functor to generalized Verma…

Let $G$ be a linear connected non-compact real simple Lie group and let $K\subset G$ be a maximal compact subgroup of $G$. Suppose that the centre of $K$ isomorphic to $\mathbb{S}^1$ so that $G/K$ is a global Hermitian symmetric space. Let…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

We give the construction of the universal, natural up to homotopy Chern-Weil differential graded algebra homomorphism: $$cw: \mathcal{I} (G) \to \Omega ^{\bullet } (BG, \mathbb{R})$$ for infinite dimensional Milnor regular Lie groups $G$,…

Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and the…

For a finite-dimensional simple Lie algebra $\mathfrak{g}$ admitting a non-trivial minuscule representation and a connected marked surface $\Sigma$ with at least two marked points and no punctures, we prove that the cluster algebra…

We introduce and study the Hilbert space of $(L^2,\Gamma,\chi)$-likewise theta functions on $\mathbb{R}^d$ with respect to a given discrete subgroup $\Gamma$ of arbitrary rank and a character $\chi$ of $\Gamma$. A concrete description is…

For any L-infinity algebra L, we construct an A-infinity structure on the space of symmetric tensors Sym*(L), which generalizes the classical universal enveloping for Lie algebras. Our construction is based on an invariant homotopy on a…

The curious connection between the spacings of the eigenvalues of random matrices and the corresponding spacings of the non trivial zeros of the Riemann zeta function is analyzed on the basis of the geometric dynamical global program of…

We investigate the well-known Loday-Quillen-Tsygan theorem, which calculates the Lie algebra homology of the general linear algebra $\mathfrak{gl}(A)$ for an associative algebra $A$ in terms of cyclic homology, and extend the proof to…

Inspired by the perspective of Reyes' noncomutative spectral theory, we attempt to develop noncommutative algebraic geometry by introducing ringed coalgebras, which can be thought of as a noncommutative generalization of schemes over a…