Related papers: On Hadamard matrices at roots of unity
Although the results are correct, it was pointed out that the results follow from some previously known results. Accordingly, this version of the paper is withdrawn by the authors.
This paper has been superseded by math.AG/0510287 and withdrawn by the author.
The paper has been withdrawn.
The paper was withdrawn because of its significant overlap with a paper appeared recently.
The paper has been withdrawn
This paper has been withdrawn by the author, due to an error in relation (11).
In this article the quantized matrix algebras as in the title have been studied at a root of unity. A full classification of simple modules over such quantized matrix algebras of rank $2$ along with a class of finite dimensional…
This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.
Daniel McNulty et.al (2024 J. Phys. A: Math. Theor. submitted) voiced suspicions to the Lemma 11(v) Part 6 in Chen and Yu (2017 J. Phys. A: Math. Theor. 50 475304) and three theorems derived in later publications (Liang et al 2019 Quantum…
This article studies the equation $[A,B]^k = {\rm Id}_n$ for matrices over $\mathbb{C}$, characterizing the pairs $(k,n)$ for which solutions exist via a classical result of Lam and Leung on sums of roots of unity. The problem is next…
This paper has been withdrawn by the author. The author found that the main results here were already obtained by K. Taniyama and A. Yasuhara `On $C$-distance of knots. Kobe J. Math. 11 (1994), no. 1, 117--127. MR1309997 (95j:57010)'. He…
Graphs are very important mathematical structures used in many applications, one of which is transportation science. When dealing with transportation networks, one deals not only with the network structure, but also with information related…
The paper is withdrawn because the analysis appeared to be incomplete.
This paper has been withdrawn by the authors.
This paper is withdrawn. We found a mistake in Lemma 4.1
This paper has been withdrawn.
The notion of root polynomials of a polynomial matrix $P(\lambda)$ was thoroughly studied in [F. Dopico and V. Noferini, Root polynomials and their role in the theory of matrix polynomials, Linear Algebra Appl. 584:37--78, 2020]. In this…
This paper has been withdrawn by the authors. It has been superseded by hep-th/0309154
A lemma by Chen et al. [J. Phys. A: Math. Theor. 50, 475304 (2017)] provides a necessary condition on the structure of any complex Hadamard matrix in a set of four mutually unbiased bases in $\mathbb{C}^6$. The proof of the lemma is shown…
This paper has been withdrawn by the author due to some error in the result