An introduction to Rota-Baxter algebra:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Somerville, Mass. [u.a.]
Internat. Press [u.a.]
2012
|
| Series: | Surveys of modern mathematics
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [211] - 221 |
| Physical Description: | X, 226 S. graph. Darst. |
| ISBN: | 9781571462534 |
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Record in the Search Index
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| adam_text | Titel: An introduction to Rota-Baxter algebra
Autor: Guo, Li
Jahr: 2012
Contents Preface ................................................vii Leitfaden .............................................. xi Part I The Operator Aspect of Rota-Baxter Algebra 1 Spitzer’s Identity ..................................... 3 1.1 Basic definitions, examples and properties................. 4 1.2 Complete Rota-Baxter algebras......................... 19 1.3 Formulations of Spitzer’s identity, old and new............. 22 1.4 Atkinson’s multiplicative decomposition and the algebraic Bogoliubov map.................................... 39 1.5 Some related literature and problems.................... 43 2 Connected Hopf Algebras and Rota-Baxter Algebras....... 47 2.1 Algebras and modules revisited......................... 48 2.2 Coalgebras and bialgebras............................ 50 2.3 Connected bialgebra and Hopf algebra.................... 54 2.4 Algebraic Birkhoff decomposition....................... 62 2.5 Some related literature and problems.................... 69 Part II The Structure Aspect of Rota-Baxter Algebra 3 Free Commutative Rota-Baxter Algebras and Shuffle Products............................................ 73 3.1 Shuffle product and generalizations...................... 74 3.2 Free commutative Rota-Baxter algebras.................. 92 3.3 Rota-Baxter algebras, Stirling numbers and partitions........107 3.4 Some related literature and problems....................116
vi Contents 4 Free Noncommutative Rota-Baxter Algebras and Rooted Trees........................................119 4.1 The Rota-Baxter algebra of trees.......................120 4.2 Free Rota-Baxter algebra on a set.......................128 4.3 Unitarization of Rota-Baxter algebras....................147 4.4 Free Rota-Baxter algebra on an algebra...................151 4.5 Some related literature and problems.....................163 Part III The Operad Aspect of Rota-Baxter Algebra 5 Rota-Baxter Algebras and Dendriform Algebras........ • 167 5.1 Concepts and basic properties..........................168 5.2 Free objects in the commutative case and shuffle products.....171 5.3 Universal enveloping algebras of tridendriform algebras.......177 5.4 Free dendriform, tridendriform algebras and free Rota-Baxter algebras................................180 5.5 Some related literature and problems....................190 6 Rota-Baxter Operators on Operads and Manin Products • • • 191 6.1 Nonsymmetric operads...............................192 6.2 Products of binary quadratic NS operads..................196 6.3 Binary quadratic ns operads from linear operators...........204 6.4 Some related literature and problems....................209 Bibliography...........................................211 Index.................................................223
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| id | DE-604.BV041367438 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:55:06Z |
| institution | BVB |
| isbn | 9781571462534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026815682 |
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| physical | X, 226 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Internat. Press [u.a.] |
| record_format | marc |
| series | Surveys of modern mathematics |
| series2 | Surveys of modern mathematics |
| spelling | Guo, Li Verfasser aut An introduction to Rota-Baxter algebra Li Guo Somerville, Mass. [u.a.] Internat. Press [u.a.] 2012 X, 226 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Surveys of modern mathematics 4 Literaturverz. S. [211] - 221 Algebraischer Ring (DE-588)4141855-4 gnd rswk-swf Freie Algebra (DE-588)4155280-5 gnd rswk-swf Algebraischer Ring (DE-588)4141855-4 s Freie Algebra (DE-588)4155280-5 s DE-604 Surveys of modern mathematics 4 (DE-604)BV041123344 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026815682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Guo, Li An introduction to Rota-Baxter algebra Surveys of modern mathematics Algebraischer Ring (DE-588)4141855-4 gnd Freie Algebra (DE-588)4155280-5 gnd |
| subject_GND | (DE-588)4141855-4 (DE-588)4155280-5 |
| title | An introduction to Rota-Baxter algebra |
| title_auth | An introduction to Rota-Baxter algebra |
| title_exact_search | An introduction to Rota-Baxter algebra |
| title_full | An introduction to Rota-Baxter algebra Li Guo |
| title_fullStr | An introduction to Rota-Baxter algebra Li Guo |
| title_full_unstemmed | An introduction to Rota-Baxter algebra Li Guo |
| title_short | An introduction to Rota-Baxter algebra |
| title_sort | an introduction to rota baxter algebra |
| topic | Algebraischer Ring (DE-588)4141855-4 gnd Freie Algebra (DE-588)4155280-5 gnd |
| topic_facet | Algebraischer Ring Freie Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026815682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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