Related papers: Graded $K$-theory and Leavitt path algebras

We determine the Gelfand-Kirillov dimension of a weighted Leavitt path algebra $L_K(E,w)$ where $K$ is a field and $(E,w)$ a finite weighted graph. Further we show that a finite-dimensional weighted Leavitt path algebra over a field $K$ is…

Let $T$ be a compact torus and $(M,\omega)$ a Hamiltonian $T$-space. We give a new proof of the $K$-theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry by using the equivariant version of the Kirwan map introduced…

Using a combinatorial approach which avoids geometry, this paper studies the ring structure of K_T(G/B), the T-equivariant K-theory of the (generalized) flag variety G/B. Here the data is a complex reductive algebraic group (or…

We calculate equivariant elliptic cohomology of the partial flag variety G/H, where H \subseteq G are compact connected Lie groups of equal rank. We identify the RO(G)-graded coefficients Ell_G^* as powers of Looijenga's line bundle and…

We compute the Borel equivariant cohomology ring of the left $K$-action on a homogeneous space $G/H$, where $G$ is a connected Lie group, $H$ and $K$ are closed, connected subgroups and $2$ and the torsion primes of the Lie groups are units…

We show that the hermitian K-theory space of a commutative ring R can be identified, up to A^1-homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-algebras, i.e., finite locally free R-algebras with…

We define Grothendieck-Witt spectra in the setting of Poincar\'e $\infty$-categories and show that they fit into an extension with a K- and an L-theoretic part. As consequences we deduce localisation sequences for Verdier quotients, and…

Leavitt path algebras associate to directed graphs a $\mathbb Z$-graded algebra and in their simplest form recover the Leavitt algebras $L(1,k)$. In this note, we first study this $\mathbb Z$-grading and characterize the ($\mathbb…

We investigate conditions under which the endomorphism ring of the Leavitt path algebra $L_{K}(E)$ possesses various ring and module-theoretical properties such as being von Neumann regular, $\pi$-regular, strongly $\pi$-regular or…

In recent work, we related the structure of subvarieties of $n\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\mathbb{C})$-orbits on the flag variety of $\mathfrak{gl}(n,\mathbb{C})$. In the first part of this…

We introduce twisted K-theoretic Gromov-Witten invariants - in the frameworks of both "ordinary" and permutation-equivariant K-theoretic GW theory defined recently by Givental. We focus on the case when the twisting is given by the Euler…

We relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K_0 classifies them completely. For arbitrary Leavitt path…

In the past, it has been shown that the Leavitt path algebra $L(E)=L_K(E)$ of a graph $E$ over a field $K$ is left and right noetherian if and only if the graph $E$ is finite and no cycle of $E$ has an exit. If $Q(E)=Q_K(E)$ denotes the…

Given an arbitrary graph E and any field K, a new class of simple left modules over the Leavitt path algebra L of the graph E over K is constructed by using vertices that emit infinitely many edges. The corresponding annihilating primitive…

Let g be a semi-simple Lie algebra. In this paper we study the spaces of based quasi-maps from the projective line P^1 to the flag variety of g (it is well-known that their singularities are supposed to model the singularities of the so…

Let $F$ be an infinite field of characteristic different from 2, and let $E$ be the Grassmann algebra of an infinite dimensional $F$-vector space $L$. In this paper we study the $\mathbb{Z}$-graded polynomial identities of $E$ with respect…

In this work, we propose to study noncommutative geometry using the language of categories of sheaves of algebras with polynomial identities and their properties, introducing new (graded) noncommutative geometries. These include, for…

In the companion paper~\cite{Gokavarapu_IJPA_2025}, we developed a classical algebraic K-theory for non-commutative $n$-ary $\Gamma$-semirings $(T,\Gamma)$ in terms of finitely generated projective $n$-ary $\Gamma$-modules and their…

We study classes determined by the Kazhdan-Lusztig basis of the Hecke algebra in the $K$-theory and hyperbolic cohomology theory of flag varieties. We first show that, in $K$-theory, the two different choices of Kazhdan-Lusztig bases…

We consider graded Cartan matrices of the symmetric groups and the Iwahori-Hecke algebras of type A, which have entries in the ring $\mathbb Z[v,v^{-1}]$. These matrices may also be interpreted as Gram matrices of the Shapovalov form on…