Related papers: A Constructive Elementary Proof of the Skolem-Noet…

We investigate the structure of the fixed-point algebra of $\mathcal{O}_n$ under the action of the cyclic permutation of the generating isometries. We prove that it is $*$-isomorphic with $\mathcal{O}_n$, thus generalizing a result of Choi…

Let k be an infinite field. Let R be the semi-local ring of a finite family of closed points on a k-smooth affine irreducible variety, let K be the fraction field of R, and let G be a reductive simple simply connected R-group scheme…

We prove that for every finitely generated subgroup of a virtually connected Lie group which admits a finite dimensional model for the classifying space for proper actions the assembly map in algebraic K-theory is split injective. We also…

It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For $F$ a non-Archimedean local field, Tupan used this to give an elementary proof that transpose…

Let $X$ be an $n$-dimensional variety over a field $k$ of characteristic zero, regular in codimension 1 with singular locus $Z$. In this paper we study the negative $K$-theory of $X$, showing that when $Z$ is sufficiently nice, $K_{1-n}(X)$…

We introduce a theory of geometry for nonnoetherian commutative algebras with finite Krull dimension. In particular, we establish new notions of normalization and height: depiction (a special noetherian overring) and geometric codimension.…

We prove that in the graded commutative ring $K_{*}(\mathbb{S})$, all positive degree elements are multiplicatively nilpotent. The analogous statements also hold for $TC_{*}(\mathbb{S};\mathbb{Z}^{\wedge}_p)$ and $K_{*}(\mathbb{Z})$.

Soibelman's theory of quantized function algebra A_q(SL_n) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally due to Kapranov and Voevodsky to…

Let $S$ be a finite dimensional noetherian scheme. For any proper morphism between smooth $S$-schemes, we prove a Riemann-Roch formula relating higher algebraic $K$-theory and motivic cohomology, thus with no projective hypothesis neither…

We introduce the notion of $GL(n)$-dependence of matrices, which is a generalization of linear dependence taking into account the matrix structure. Then we prove a theorem, which generalizes, on the one hand, the fact that $n+1$ vectors in…

A polynomial has saturated Newton polytope (SNP) if every lattice point of the convex hull of its exponent vectors corresponds to a monomial. We compile instances of SNP in algebraic combinatorics (some with proofs, others conjecturally):…

For a finite dimensional monomial algebra $\Lambda$ over a field $K$ we show that the Hochschild cohomology ring of $\Lambda$ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated $K$-algebra of…

We prove that for a complete quasivariety $K$ of topological $E$-algebras of countable discrete signature $E$ and each submetrizable $ANR(k_\omega)$-space $X$ its free topological $E$-algebra $F_K(X)$ in the class $K$ is a submetrizable…

We show that a monomial algebra $\Lambda$ over an algebraically closed field $K$ is self-injective if and only if each map $\mathrm{soc}(_{\Lambda}\Lambda)\to \ _{\Lambda}\Lambda$ can be extended to an endomorphism of $_{\Lambda}\Lambda$,…

In this paper we identify the ``nil-terms'' for Waldhausen's algebraic K-theory of spaces functor as the reduced K-theory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.

The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra A over an algebraically closed field F, such that its group scheme of automorphisms is smooth, is shown to be…

Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism F, we denote by k(X)^F its field of invariants, i.e. the set of rational functions f on X such that f(F)=f. Let n(F)…

We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensaetze) from real algebraic geometry can be generalized to noncommutative $*$-algebras. A…

By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…

A non-associative algebra over a field $\mathbb{K}$ is a $\mathbb{K}$-vector space $A$ equipped with a bilinear operation \[ {A\times A\to A\colon\; (x,y)\mapsto x\cdot y=xy}. \] The collection of all non-associative algebras over…