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Q&A for professional mathematicians
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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
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Association of a Catalan Triangle with Quaternions and Octonions?
The OEIS entry A053121 for a version of the Catalan triangle related to the expansion of the monomials $x^n$ in the Chebyshev polynomials of the second kind $U_k(x/2)$ references p. 60 of On Quaternions and Octonions by J. H. Conway and D. A. Smith ...
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Poincaré Reducibility Isogeny Degree
Suppose that $(X, H)$ is a polarized abelian variety. Suppose furthermore that $A \subset X$ is an abelian subvariety. Then by Poincaré reducibility there is a complementary abelian subvariety $B$ such that the addition map is an isogeny $a \colon A...
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Non isomorphic Cayley digraphs of the dicyclic groups of orders eight [aka Quate...
I. About the Quaternion group [the dicyclic group of order 8].
According to this paper Enumeration of dicirculant digraphs, Jing Wang et all, [see table one at page 13] the dicyclic group of order 8 has two non isomorphic connected Cayley digraphs.
Also Scott Effler in his thesis about two-generated Cayley digraphs [see tables in the thesis] says that there are four non isomorphic Cayley Digraphs of order eight with permutation representation of degree eight. There are two groups of order eight... -
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"One-sided" localization of abelian categories
Let $A$ be an abelian category and $S$ be a right multiplicative system, that is, a collection of morphisms in $S$ satisfying: (MS1) the identity morphisms of all objects in $A$ belong to $S$ and $S$ is closed under composition, (RMS2) if $s:Y\to Z$...
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