• Title/Summary/Keyword: q-commuting

Search Result 11, Processing Time 0.023 seconds

A PARTITION OF q-COMMUTING MATRIX

  • Eunmi Choi
    • East Asian mathematical journal
    • /
    • v.39 no.3
    • /
    • pp.279-290
    • /
    • 2023
  • We study divisibilities of elements in the q-commuting matrix C(q). We first make a coefficient matrix Ĉ of C(q) which is independent of q, study divisibilities over Ĉ and then retrieve our findings to C(q). Finally we partition the C(q) into 2 × 2 block matrices.

q-COEFFICIENT TABLE OF NEGATIVE EXPONENT POLYNOMIAL WITH q-COMMUTING VARIABLES

  • Choi, Eunmi
    • Korean Journal of Mathematics
    • /
    • v.30 no.3
    • /
    • pp.433-442
    • /
    • 2022
  • Let N(q) be an arithmetic table of a negative exponent polynomial with q-commuting variables. We study sequential properties of diagonal sums of N(q). We first device a q-coefficient table $\hat{N}$ of N(q), find sequences of diagonal sums over $\hat{N}$, and then retrieve the findings of $\hat{N}$ to N(q). We also explore recurrence rules of s-slope diagonal sums of N(q) with various s and q.

ON COMMUTING GRAPHS OF GROUP RING ZnQ8

  • Chen, Jianlong;Gao, Yanyan;Tang, Gaohua
    • Communications of the Korean Mathematical Society
    • /
    • v.27 no.1
    • /
    • pp.57-68
    • /
    • 2012
  • The commuting graph of an arbitrary ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity, the diameter, the maximum degree and the minimum degree of the commuting graph of group ring $Z_nQ_8$. The main result is that $\Gamma(Z_nQ_8)$ is connected if and only if n is not a prime. If $\Gamma(Z_nQ_8)$ is connected, then diam($Z_nQ_8$)= 3, while $\Gamma(Z_nQ_8)$ is disconnected then every connected component of $\Gamma(Z_nQ_8)$ must be a complete graph with a same size. Further, we obtain the degree of every vertex in $\Gamma(Z_nQ_8)$, the maximum degree and the minimum degree of $\Gamma(Z_nQ_8)$.

ON k SLOPE DIAGONAL SUMS OF q-COMMUTING TABLE AND NONZERO PAULI TABLE

  • Choi, Eunmi;Choi, MyungJin
    • East Asian mathematical journal
    • /
    • v.36 no.3
    • /
    • pp.425-435
    • /
    • 2020
  • We explore the Pauli table C(-1) and nonzero Pauli table W. Recurrence rules and interrelationships of any k slope diagonal sums over C(-1) and W are studied in connection with diagonal sums of the Pascal table C(1). Since diagonal sums of C(1) are Fibonacci numbers, any k slope diagonal sums over C(-1) and W are explained by Fibonacci numbers.

HIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA μq(gl(m, n))

  • Moon, Dong-Ho
    • Journal of the Korean Mathematical Society
    • /
    • v.40 no.1
    • /
    • pp.1-28
    • /
    • 2003
  • The Iwahori-Hecke algebra $H_{k}$ ( $q^2$) of type A acts on the k-fold tensor product space of the natural representation of the quantum superalgebra (equation omitted)$_{q}$(gl(m, n)). We show the Hecke algebra $H_{k}$ ( $q^2$) and the quantum superalgebra (equation omitted)$_{q}$(gl(m n)) have commuting actions on the tensor product space, and determine the centralizer of each other. Using this result together with Gyoja's q-analogue of the Young symmetrizers, we construct highest weight vectors of irreducible summands of the tensor product space.

ON LOCAL SPECTRAL PROPERTIES OF RIESZ OPERATORS

  • JONG-KWANG YOO
    • Journal of applied mathematics & informatics
    • /
    • v.41 no.2
    • /
    • pp.273-286
    • /
    • 2023
  • In this paper we show that if T ∈ L(X) and S ∈ L(X) is a Riesz operator commuting with T and XS(F) ∈ Lat(S), where F = {0} or F ⊆ ℂ ⧵ {0} is closed then T|XS(F) and T|XT(F) + S|XS(F) share the local spectral properties such as SVEP, Dunford's property (C), Bishop's property (𝛽), decomopsition property (𝛿) and decomposability. As a corollary, if T ∈ L(X) and Q ∈ L(X) is a quasinilpotent operator commuting with T then T is Riesz if and only if T + Q is Riesz. We also study some spectral properties of Riesz operators acting on Banach spaces. We show that if T, S ∈ L(X) such that TS = ST, and Y ∈ Lat(S) is a hyperinvarinat subspace of X for which 𝜎(S|Y ) = {0} then 𝜎*(T|Y + S|Y ) = 𝜎*(T|Y ) for 𝜎* ∈ {𝜎, 𝜎loc, 𝜎sur, 𝜎ap}. Finally, we show that if T ∈ L(X) and S ∈ L(Y ) on the Banach spaces X and Y and T is similar to S then T is Riesz if and only if S is Riesz.

COMMON FIXED POINT AND INVARIANT APPROXIMATION IN MENGER CONVEX METRIC SPACES

  • Hussain, Nawab;Abbas, Mujahid;Kim, Jong-Kyu
    • Bulletin of the Korean Mathematical Society
    • /
    • v.45 no.4
    • /
    • pp.671-680
    • /
    • 2008
  • Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in a Menger convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various well known results.

GENERALIZED SKEW DERIVATIONS AS JORDAN HOMOMORPHISMS ON MULTILINEAR POLYNOMIALS

  • De Filippis, Vincenzo
    • Journal of the Korean Mathematical Society
    • /
    • v.52 no.1
    • /
    • pp.191-207
    • /
    • 2015
  • Let $\mathcal{R}$ be a prime ring of characteristic different from 2, $\mathcal{Q}_r$ be its right Martindale quotient ring and $\mathcal{C}$ be its extended centroid. Suppose that $\mathcal{G}$ is a nonzero generalized skew derivation of $\mathcal{R}$, ${\alpha}$ is the associated automorphism of $\mathcal{G}$, f($x_1$, ${\cdots}$, $x_n$) is a non-central multilinear polynomial over $\mathcal{C}$ with n non-commuting variables and $$\mathcal{S}=\{f(r_1,{\cdots},r_n)\left|r_1,{\cdots},r_n{\in}\mathcal{R}\}$$. If $\mathcal{G}$ acts as a Jordan homomorphism on $\mathcal{S}$, then either $\mathcal{G}(x)=x$ for all $x{\in}\mathcal{R}$, or $\mathcal{G}={\alpha}$.