We study the category Rep (Q, F 1) Rep(Q,F_1) of representations of a quiver Q over “the
field with one element”, denoted by F 1 F_1, and the Hall algebra of Rep (Q, F 1) …

A quiver representation assigns a vector space to each vertex, and a linear map to each
arrow of a quiver. When one considers the category-representations of a quiver with …

We study the algebraic K-theory and Grothendieck–Witt theory of proto-exact categories of
vector bundles over monoid schemes. Our main results are the complete description of the …

Proto-exact categories, introduced by Dyckerhoff and Kapranov, are a generalization of
Quillen exact categories which provide a framework for defining algebraic K-theory and Hall …

We study the algebraic $ K $-theory and Grothendieck-Witt theory of proto-exact categories
of vector bundles over monoid schemes. Our main results are the complete description of …

Green's theorem states that the Hall algebra of the category of representations of a quiver
over a finite field is a twisted bialgebra. Considering instead categories of orthogonal or …

We associate to a projective n-dimensional toric variety X Δ a pair of co-commutative (but
generally non-commutative) Hopf algebras HX α, HXT. These arise as Hall algebras of …

Jun, Jaiung ; Szczesny, Matt ; Tolliver, Jeffrey Proto-exact categories of modules over semirings
and hyperrings. (English) £ Page 1 Jun, Jaiung; Szczesny, Matt; Tolliver, Jeffrey Proto-exact …

We study commutative ring structures on the integral span of rooted trees and n-dimensional
skew shapes. The multiplication in these rings arises from the smash product operation on …

We study commutative ring structures on the integral span of rooted trees and n-dimensional
skew shapes. The multiplication in these rings arises from the smash product operation on …