JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 79-84.doi: 10.6040/j.issn.1671-9352.0.2019.192

Previous Articles    

Higher ξ-Lie derivable maps on triangular algebras at reciprocal elements

ZHANG Xia, ZHANG Jian-hua*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2019-10-12

PDF (PC)

355

Abstract: Let U=Tri(A,M,B )be a triangular algebra with identity 1, 1A,1B be the unit of A and B, respectively. For any A∈A, B∈B, there are integers k1,k2 respectively, making k11A-A, k21B-B invertible in triangular algebras. {φn}n∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φn}n∈N satisfies φn(［U,V］ξ)=∑i+j=nφi(U)φj(V)-ξφi(V)φj(U)(ξ≠0,1), for any U,V∈U with UV=VU=1, then {φn}n∈N is a higher derivation, where φ0=id0 is the identity map, ［U,V］ξ=UV-ξVU.

Key words: triangular algebra, higher ξ-Lie derivable map, higher derivation

CLC Number: 

  • O177.1
[1] ZHAO Jinping, ZHU Jun. Jordan higher all-derivable points in triangular algerbras[J]. Linear Algebra Appl, 2012, 436(9):3072-3086.
[2] LIU Dan, ZHANG Jianhua. Jordan higher derivable maps on triangular algebras by commutative zero products[J]. Acta Math Sinica, 2016, 32(2):258-264.
[3] ZENG Hongyan, ZHU Jun. Jordan higher all-derivable points on nontrivial nest algebra[J]. Linear Algebra Appl, 2011, 434(2):463-474.
[4] ZHEN Nannan, ZHU Jun. Jordan higher all-derivable points in nest algebras[J]. Taiwanese Journal of Mathematics, 2012, 16(6):1959-1970.
[5] 费秀海, 张建华. 三角代数上零点处的高阶ξ-Lie可导映射[J]. 陕西师范大学学报(自然科学版), 2015, 43(3):6-9. FEI Xiuhai, ZHANG Jianhua. Higher ξ-Lie derivable maps on triangular algebras at zero point[J]. Journal of Shannxi Normal University(Natural Science), 2015, 43(3):6-9.
[6] XIAO Zhankui, WEI Feng. Jordan higher derivations on triangular algebra[J]. Linear Algebra Appl, 2010, 432(1):2615-2622.
[7] LI Jiankui, ZHOU Jiren. Characterizations of Jordan derivations and Jordan homomorphisms[J]. Linear and Multilinear Algebra, 2011, 59(3):193-204.
[8] AN Runling, HOU Jinchuan. Characterizations of derivations on triangular rings: additive maps derivable at idempotents[J]. Linear Algebra Appl, 2009, 431(5/6/7):1070-1080.
[9] MIZAVAZIRI M. Characterization of higher derivations on algebras[J]. Communications in Algebra, 2010, 38(3):981-987.
[10] QI Xiaofei, HOU Jinchuan. Additive Lie(ξ-Lie)derivations and generalized Lie(ξ-Lie)derivations on nest algebras[J]. Linear Algebra Appl, 2009, 431(5/6/7):843-854.
[11] JI Peisheng, QI Weiqing. Characterizations of Lie derivations of triangular algebras[J]. Linear Algebra Appl, 2011, 435(5):1137-1146.
[12] QI Xiaofei, CUI Jianlian, HOU Jinchuan. Characterizing additive ξ-Lie derivations of prime algebras by ξ-Lie zero products[J]. Linear Algebra Appl, 2011, 434(3):669-682.
[13] ZHANG Xu, AN Runling, HOU Jinchuan. Characterizations of higher derivations on CLS algerbras[J]. Epo Math, 2013, 31(4):392-404.
[1] FEI Xiu-hai, ZHANG Jian-hua. Linear maps on triangular algebras for which the space of all inner derivations is Lie invariant [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 79-83.
[2] WU Li, ZHANG Jian-hua. Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 42-47.
[3] HU Li-xia, ZHANG Jian-hua. Lie higher derivable mappings of triangular algebras at zero points [J]. J4, 2013, 48(4): 5-9.
[4] JI Pei-sheng,QI Wei-qing,LIU Zhong-yan . Jordan ideals in triangular algebras of type II1 hyper-finite factors [J]. J4, 2008, 43(4): 6-08 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd