{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:fec421d2-e46d-4258-acc3-ef2dfb231874", "labels": { "zh-CN": "外代数", "en": "exterior algebra" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "0a2655a2540ce5c72efcccf9fad016f44128a638edca47a85996ba27e7075e62", "occurrences": [ { "concept_id": "urn:uuid:fec421d2-e46d-4258-acc3-ef2dfb231874", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-06/04-grassmann-algebras", "anchor": "concept-6-exterior-algebra", "chapter": "6", "section": "6.4", "offset": 10536, "range": [ 15862, 16099 ], "source_revision": "32eeacc9d191d1731e166539ce97d97692e810e41c7d779ab660622f75a05e9f", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "外代数(exterior algebra)", "context": { "range": [ 15578, 16100 ], "quote": "性质(EP3)使$\\Lambda ( V )$关于外积构成一个代数，称为$V$上的格拉斯曼代数(Grassmann algebra)或外代数(exterior algebra)。", "quote_sha256": "28bab0a7a18173c13fd36c3e53437149396d0648637e87420a10783c9d3e1bf2", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-06/04-grassmann-algebras", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-a9d19efb3e9b20d080b3d8e8" }, { "concept_id": "urn:uuid:fec421d2-e46d-4258-acc3-ef2dfb231874", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-06/04-grassmann-algebras", "anchor": "first-6cac602420dc2ecf58ec-en", "chapter": "6", "section": "6.4", "offset": 13603, "range": [ 18421, 18656 ], "source_revision": "d6ff3d1952b0a1a8362984090aee9f4003edaa40ea9a3d639daff8f5ab34f57f", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "exterior algebra", "context": { "range": [ 18083, 18666 ], "quote": "Property (EP3) makes $\\Lambda ( V )$ into an algebra with respect to exterior product, called the Grassmann algebra or exterior algebra over $V$.", "quote_sha256": "844411623852fd7783eef9bdc671508b02e18d20de79d4f41b22f7ef243904a1", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "zh/chapter-06/04-grassmann-algebras", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-57b19fbdce00874db4f572b7" }, { "concept_id": "urn:uuid:fec421d2-e46d-4258-acc3-ef2dfb231874", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-08/03-exterior-product", "anchor": "xref-03-exterior-product-1", "chapter": "8", "section": "8.3", "offset": 2521, "range": [ 7437, 7642 ], "source_revision": "fbc24c37fc59e432d6b22bcfaf67b2112fbdfae32171ae39930e3ccebe641b2d", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "外代数(exterior algebra)", "context": { "range": [ 7392, 7687 ], "quote": "因此，带有楔积的空间 $\\Lambda ( V )$ 是一个结合代数，称为 $V$ 上的 外代数(exterior algebra)。书写诸如 $A \\land B \\land C$ 这样的表达式没有歧义。由于外积具有性质", "quote_sha256": "a906f42c98c79fbbe528ccab6ee033bfe654b69013cc58b0e2a160f8f3a9dab0", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-08/03-exterior-product", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-cc656491372cbc7db102208a" }, { "concept_id": "urn:uuid:fec421d2-e46d-4258-acc3-ef2dfb231874", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-08/03-exterior-product", "anchor": "xref-03-exterior-product-2", "chapter": "8", "section": "8.3", "offset": 2993, "range": [ 7441, 7641 ], "source_revision": "2f11f5485cdd0333f252dbf2c62083b8b2e4142d7e96810e7b7f645db051856f", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "exterior algebra", "context": { "range": [ 7348, 7770 ], "quote": "The space $\\Lambda ( V )$ with wedge product is therefore an associative algebra, called the exterior algebra over $V$. 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