COMMUTING MAPS: A SURVEY

By Matej Breˇsar. 2004

263 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2bcf6d5e6455673632cef7f54a9dbdbcc76ee512

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Xiaomin Tang
2. Guangzhe Fan
3. Xiansheng Dai
4. Chunguang Xia
5. M. Brevsar
6. Kaiming Zhao
7. Zhengxin Chen
8. Xiu Han

Citations in the corpus

• Biderivations and linear commuting maps on simple generalized Witt algebras over a field (2016, unknown): “We encourage the reader to read the well-written survey paper [4].”
• Super-biderivations of Lie superalgebras (2016, background): “generalized derivations are very important subjects in the research of both algebras and their generalizations. In recent years, biderivations have aroused many scholars’ great interests in [1–8]. In [2, 3], Breˇsar et al showed that all biderivations on commutative prime rings are inner bidrivation”
• Biderivations and Commuting Linear Maps on Lie Algebras (2018, background): “ds that we will employ. The study of commuting maps and (skew-symmetric) biderivations has its roots in associative ring theory [2, 5], where it has turned out to be influential and far-reaching – see [3] and [4]. An interest in studying these maps on Lie algebras has grown more recently [6, 11, 9, 1”
• On multiplicative (generalized)-derivations in prime and semiprime rings (2013, background): “There has been considerable interest in commuting and centralizing maps in prime and semiprime rings (see for example [6] and [9], where further references can be found).”
• Linear Super-Commuting Maps and Super-Biderivations on the Super-Virasoro Algebras (2016, methodology): “We refer the reader to the survey paper by Brešar [4] for a detailed discussion and an extensive bibliography.”
• Biderivations And Linear Commuting Maps on the Schrödinger-Virasoro Lie Algebra (2013, background): “The author of [2] showed that commuting maps on an associative algebra have”
• Biderivations of finite-dimensional complex simple Lie algebras (2016, background): “x),x] = 0 for any x∈ L. The first important result on linear (or additive ) commuting maps is Posners theorem [15] from 1957. Then many scholars study commuting maps on all kinds of algebra structures [1, 3, 4, 7, 8, 11, 13, 16, 18, 20]. In particular, Breˇsar have been proposed briefly discuss variou”
• Biderivations of the Parabolic Subalgebras of Simple Lie Algebras (2011, background): “Because biderivations have many applications to other fields (see [2, 5] for details, where applications of biderivations to other fields are described), we are encouraged to transfer the concept of biderivation from associative algebras to Lie algebras.”
• Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras (2017, background): “Brešar [6] brie y discuss various extensions of the notion of a commuting map.”