A norm functor for quadratic algebras - Biesel, Owen (Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2022)
Given commutative, unital rings $$\mathcal {A}$$and $$\mathcal {B}$$with a ring homomorphism $$\mathcal {A}\rightarrow \mathcal {B}$$making $$\mathcal {B}$$free of finite rank as an $$\mathcal {A}$$-module, we can ask for a “trace” or “norm” homomorphism taking algebraic data over $$\mathcal {B}$$to algebraic data over $$\mathcal {A}$$. In this paper we we construct a norm functor for the data of a quadratic algebra: given a locally-free rank-2 $$\mathcal {B}$$-algebra $$\mathcal {D}$$, we produce a locally-free rank-2 $$\mathcal {A}$$-algebra $$\textrm{Nm}_{\mathcal {B}/\mathcal {A}}(\mathcal {D})$$in a way that is compatible with other norm functors and which extends a known construction for étale quadratic algebras. We also conjecture a relationship between discriminant algebras and this new norm functor.
0 citations (Crossref) [2023-10-31]
Keywords: 11R11; 13B02; 13B40; 13C10; 14B25; Algebra of finite rank; Norm functor; Quadratic algebra; Ring extension; dept.mat; Étale algebra

Deformations of reducible SL(n, C) representations of fibered 3-manifold groups - Kozai, K. (Osaka Journal of Mathematics, 2022)
Let Mφ be a surface bundle over a circle with monodromy φ: S → S. We study deformations of certain reducible representations of π1(Mφ)intoSL(n, C), obtained by composing a reducible representation into SL(2, C) with the irreducible representation SL(2, C) → SL(n, C). In particular, we show that under certain conditions on the eigenvalues of φ∗, the reducible representation is contained in a (n + 1 + k)(n − 1) dimensional component of the representation variety, where k is the number of components of ∂Mφ . This result applies to mapping tori of pseudo-Anosov maps with orientable invariant foliations whenever 1 is not an eigenvalue of the induced map on homology, where the reducible representation is also a limit of irreducible representations. © 2022, Osaka University. All rights reserved.
Keywords: dept.mat; ⛔ No DOI found

Constructing (3, B)-sudoku pair latin squares - Carrigan, Braxton; Diaz, David; Hammer, James; Lorch, John (Australasian Journal of Combinatorics, 2022)
An (a, b)-Sudoku pair Latin square is a Latin square that is simult-aneously an (a, b)-Sudoku Latin square and a (b, a)-Sudoku Latin square. While (a, b)-Sudoku Latin squares are known to exist for any positive integers a and b, the pairs a, b for which an (a, b)-Sudoku pair Latin square exists are largely unknown. In this article we establish the existence of (a, b)-Sudoku pair Latin squares for an infinite collection of pairs (a, b). Our results show that a (3, b)-Sudoku pair Latin square can be constructed for any positive integer b. ©The author(s).
Type: Article tex.citation: https://api.elsevier.com/content/abstract/scopus_id/85121634938
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found