Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Submit a Manuscript
- Table of Contents
ISRN Algebra
Volume 2011 (2011), Article ID 247403, 11 pages
doi:10.5402/2011/247403
Research Article
A New Proof of the Existence of Free Lie Algebras and an Application
Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
Received 23 March 2011; Accepted 20 April 2011
Academic Editors: K. Dekimpe and J. Kakol
Copyright © 2011 Andrea Bonfiglioli and Roberta Fulci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- N. Bourbaki, βÉléments de Mathématique, Fasc. XXXVII: Groupes et Algèbres de Lie, Chap. II: Algèbres de Lie, Chap. III: Groupes de Lie,β in Actualités Scientifiques et Industrielles, vol. 1349, Hermann, Paris, France, 1972.
- C. Reutenauer, Free Lie Algebras, vol. 7 of London Mathematical Society Monographs, Clarendon Press, Oxford, UK, 1993.
- N. Bourbaki, βÉléments de Mathématique, Fasc. XXVI: Groupes et Algèbres de Lie, Chap. I: Algèbres de Lie,β in Actualités Scientifiques et Industrielles, vol. 1285, Hermann, Paris, France, 1960.
- G. P. Hochschild, The Structure of Lie Groups, Holden-Day, San Francisco, Calif, USA, 1965.
- J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, vol. 9 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1980.
- N. Jacobson, Lie Algebras, vol. 10 of Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers, John Wiley and Sons, New York, NY, USA, 1962.
- V. S. Varadarajan, Lie groups, Lie Algebras, and Their Representations, vol. 102 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1984.
- A. Bonfiglioli and R. Fulci, Topics in Noncommutative Algebra. The Theorem of Campbell, Baker, Hausdorff and Dynkin, Lecture Notes in Mathematics, Springer, Berlin, Germany, 2011.
- P. Cartier, βDémonstration algébrique de la formule de Hausdorff,β Bulletin de la Société Mathématique de France, vol. 84, pp. 241β249, 1956. View at Zentralblatt MATH
- J. P. Serre, Lie Algebras and Lie Groups, Lectures Given at Harvard University, W. A. Benjamin, New York, NY, USA, 1st edition, 1964.
- J. P. Serre, Lie Algebras and Lie Groups, vol. 1500 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, Germany, 2nd edition, 1965.
- F. Hausdorff, βDie symbolische exponentialformel in der gruppentheorie,β Leipzig Berichte, vol. 58, pp. 19β48, 1906.
- M. Eichler, βA new proof of the Baker-Campbell-Hausdorff formula,β Journal of the Mathematical Society of Japan, vol. 20, pp. 23β25, 1968. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- D. Ž. Djoković, βAn elementary proof of the Baker-Campbell-Hausdorff-Dynkin formula,β Mathematische Zeitschrift, vol. 143, no. 3, pp. 209β211, 1975. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- E. B. Dynkin, βCalculation of the coefficients in the Campbell-Hausdorff formula,β Doklady Akademii Nauk SSSR, vol. 57, pp. 323β326, 1947.
- W. Specht, βDie linearen Beziehungen zwischen höheren Kommutatoren,β Mathematische Zeitschrift, vol. 51, pp. 367β376, 1948. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- F. Wever, βOperatoren in lieschen ringen,β Journal für die Reine und Angewandte Mathematik, vol. 187, pp. 44β55, 1949. View at Zentralblatt MATH