• 제목/요약/키워드: inner derivation

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INNER DERIVATIONS MAPPING INTO THE RADICAL

  • Jun, Kil-Woung;Lee, Young-Whan
    • Journal of applied mathematics & informatics
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    • 제5권3호
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    • pp.889-893
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    • 1998
  • In this paper we show that $\sigma$a maps into the radical if and only if for every irreducible representation $\pi$,$\pi$(a) is scalar and obtain that every inner derivation corresponding to $\sigma$-quasi central elements in some Banach algebra maps into the radical.

DERIVATIONS ON CONVOLUTION ALGEBRAS

  • MEHDIPOUR, MOHAMMAD JAVAD;SAEEDI, ZAHRA
    • 대한수학회보
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    • 제52권4호
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    • pp.1123-1132
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    • 2015
  • In this paper, we investigate derivations on the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$. We then show that a derivation on $L^{\infty}_0({\omega})^*$ is continuous if and only if its restriction to rad($L^{\infty}_0({\omega})^*$) is continuous. We also prove that there is no nonzero centralizing derivation on $L^{\infty}_0({\omega})^*$. Finally, we prove that the space of all inner derivations of $L^{\infty}_0({\omega})^*$ is continuously homomorphic to the space $L^{\infty}_0({\omega})^*/L^1({\omega})$.

ON DERIVATIONS IN NONCOMMUTATIVE SEMISIMPLE BANACH ALGEBRAS

  • Jung, Yong-Soo
    • 대한수학회보
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    • 제35권3호
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    • pp.583-590
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    • 1998
  • The purpose of this paper is to prove the following results: Let A be a noncommutative semisimple Banach algebra. (1) Suppose that a linear derivation D : A $\to A$ is such that [D(x),x]x=0 holds for all $x \in A$. Then we have D=0. (2) Suppose that a linear derivation $D:A\to A$ is such that $D(x)x^2 + x^2D(x)=0$ holds for all $x \in A$. Then we have C=0.

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(σ, σ)-DERIVATION AND (σ, 𝜏)-WEAK AMENABILITY OF BEURLING ALGEBRA

  • Chen, Lin;Zhang, Jianhua
    • 대한수학회보
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    • 제58권5호
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    • pp.1209-1219
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    • 2021
  • Let G be a topological group with a locally compact and Hausdorff topology. Let ω be a diagonally bounded weight on G. In this paper, (σ, σ)-derivation and (σ, 𝜏)-weak amenability of the Beurling algebra L1ω(G) are studied, where σ, 𝜏 are isometric automorphisms of L1ω(G). We prove that every continuous (σ, σ)-derivation from L1ω(G) into measure algebra Mω(G) is (σ, σ)-inner and the Beurling algebra L1ω(G) is (σ, 𝜏)-weakly amenable.

On complete Lie superalgebras

  • Chun, Jang-Ho;Lee, Jong-Sook
    • 대한수학회논문집
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    • 제11권2호
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    • pp.323-334
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    • 1996
  • This paper is concerned with the equivalent conditions, the decomposition and the uniqueness of complete Lie superalgebras and a complete Lie superalgebra Derg.

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Efficient Derivation of New Human Embryonic Stem Cell Lines

  • Kim, Sun Jong;Lee, Jeoung Eun;Park, Jong Hyuk;Lee, Jung Bok;Kim, Jin Mee;Yoon, Byung Sun;Song, Ji Min;Roh, Sung Il;Kim, Chul Geun;Yoon, Hyun Soo
    • Molecules and Cells
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    • 제19권1호
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    • pp.46-53
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    • 2005
  • Human embryonic stem (hES) cells, unlike most cells derived from adult or fetal human tissues, represent a potentially unlimited source of various cell types for basic clinical research. To meet the increased demand for characterized hES cell lines, we established and characterized nine new lines obtained from frozen-thawed pronucleus-stage embryos. In addition, we improved the derivation efficiency from inner cell masses (to 47.4%) and optimized culture conditions for undifferentiated hES cells. After these cell lines had been maintained for over a year in vitro, they were characterized comprehensively for expression of markers of undifferentiated hES cells, karyotype, and in vitro/in vivo differentiation capacity. All of the cell lines were pluripotent, and one cell line was trisomic for chromosome 3. Improved culture techniques for hES cells should make them a good source for diverse applications in regenerative medicine, but further investigation is needed of their basic biology.

MODULE DERIVATIONS ON COMMUTATIVE BANACH MODULES

  • Amini, Massoud;Bodaghi, Abasalt;Shojaee, Behrouz
    • 대한수학회논문집
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    • 제35권3호
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    • pp.891-906
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    • 2020
  • In this paper, the commutative module amenable Banach algebras are characterized. The hereditary and permanence properties of module amenability and the relations between module amenability of a Banach algebra and its ideals are explored. Analogous to the classical case of amenability, it is shown that the projective tensor product and direct sum of module amenable Banach algebras are again module amenable. By an application of Ryll-Nardzewski fixed point theorem, it is shown that for an inverse semigroup S, every module derivation of 𝑙1(S) into a reflexive module is inner.

NOTES ON A NON-ASSOCIATIVE ALGEBRAS WITH EXPONENTIAL FUNCTIONS I

  • CHOI, SEUL HEE
    • 호남수학학술지
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    • 제28권2호
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    • pp.197-204
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    • 2006
  • For the evaluation algebra $F[e^{{\pm}{\chi}}]_M$, if M={$\partial$}, the automorphism group $Aut_{non}$($F[e^{{\pm}{\chi}}]_M$) and $Der_{non}$($F[e^{{\pm}{\chi}}]_M$) of the evaluation algebra $F[e^{{\pm}{\chi}}]_M$ are found in the paper [12]. For M={${\partial}^n$}, we find $Aut_{non}$($F[e^{{\pm}{\chi}}]_M$) and $Der_{non}$($F[e^{{\pm}{\chi}}]_M$) of the evaluation algebra $F[e^{{\pm}{\chi}}]_M$ in this paper. We show that a derivation of some non-associative algebra is not inner.

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A REMARK ON WEAK MODULE-AMENABILITY IN BANACH ALGEBRAS

  • Mirmostafaee, Alireza Kamel;Rahpeyma, Omid Pourbahri
    • 호남수학학술지
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    • 제43권2호
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    • pp.209-219
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    • 2021
  • We define a new concept of module amenability which is compatible with original definition of amenability. For a module dual algebra 𝓐, we will show that if every module derivation D : 𝓐** → J𝓐** is inner then 𝓐 is weak module amenable. Moreover, we will prove that under certain conditions, weak module amenability of 𝓐** implies weak module amenability of 𝓐.