arXiv subjects

Suyash Srivastava

Publications and source records attributed to Suyash Srivastava.

3 recordsLinked to original sources

arXiv2024

Cantor-Schröder-Bernstein theorem for a class of countable linear orders

The shuffle of a non-empty countable set $ S $ of linear orders is the (unique up to isomorphism) linear order $ Ξ(S) $ obtained by fixing a coloring function $ χ: \mathbb{Q} \to S $ having fibers dense in $ \mathbb{Q} $ and replacing each rational $ q $ in $ (\mathbb{Q}, <) $ with an isomorphic copy of $ χ(q) $. We prove that any two countable shuffles that embed as convex subsets into each other are order isomorphic.

math.LO↗

arXiv2024

Automating the stable rank computation for special biserial algebras

Given a special biserial algebra $Λ$ over an algebraically closed field, let $\mathrm{rad}_Λ$ denote the radical of its module category. The authors showed with Sinha that the stable rank of a special biserial algebra $Λ$, i.e., the least ordinal $γ$ satisfying $\mathrm{rad}_Λ^γ=\mathrm{rad}_Λ^{γ+1}$, is strictly bounded above by $ω^2$. We use finite automata to give simple algorithmic proofs, complete with their time complexity analyses, of two key ingredients in the proof of this result--the first one states that certain linear orders called hammocks associated with such algebras are \emph{finite description linear orders}, i.e., they lie in the smallest class of linear orders that contains finite linear orders and $ω$, and that is closed under isomorphisms, order-reversals, binary sums, co-lexicographic products and finitary shuffles. We also document a complete proof of the result that the class of order types(=order-isomorphism classes) of finite description linear orders coincides with that of languages of finite automata under inorder.

math.RT↗

arXiv2023

On the stable radical of the module category for special biserial algebras

Suppose $Λ$ is a special biserial algebra over an algebraically closed field. Schröer showed that if $Λ$ is domestic then the radical of the category of finitely generated (left) $Λ$-modules is nilpotent, and the least ordinal, denoted $\mathrm{st}(Λ)$, where the decreasing sequence of powers of the radical stabilizes satisfies $\mathrm{st}(Λ)<ω^2$. With Gupta and Sardar, the third author conjectured that if $Λ$ has at least one band then $ω\le\mathrm{st}(Λ)<ω^2$ even when $Λ$ is non-domestic. In this paper we settle this conjecture in the affirmative. We also describe an algorithm to compute $\mathrm{st}(Λ)$ up to a finite error. We also show that for each $ω\leqα<ω^2$ there is a finite-dimensional tame representation type algebra $Γ$ with $\mathrm{st}(Γ)=α$.

math.RT↗