{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:7c7d436a-933b-40b7-9fbb-45f0ff035eec", "labels": { "zh-CN": "单参数子群", "en": "one-parameter subgroup" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "ac61ef355bd1716c7eeaac96e7307343a3bc7c6eefe61b40a0851c3af902c583", "occurrences": [ { "concept_id": "urn:uuid:7c7d436a-933b-40b7-9fbb-45f0ff035eec", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-06/05-lie-algebras-and-lie-groups", "anchor": "concept-6-one-parameter-subgroup", "chapter": "6", "section": "6.5", "offset": 12094, "range": [ 19181, 19432 ], "source_revision": "46a8514fc1659203f37a413780dc7b144eb121d7587e2bdcd4e8f324bc97ab90", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "单参数子群(one-parameter subgroup)", "context": { "range": [ 19172, 19677 ], "quote": "李群 $G$ 的 单参数子群(one-parameter subgroup) 是实数加法群到 $G$ 的同态 $\\varphi : \\mathbb { R } \\to G$ 的像 $\\varphi ( \\mathbb { R } )$。将矩阵李群的单参数子群的元素简单地写成 $\\begin{array} { r } { { \\bf A } ( t ) = \\Gamma \\big ( a ^ { 1 } ( t ) , a ^ { 2 } ( t ) , \\dots , a ^ { n } ( t ) \\big ) } \\end{array}$ 时，同态性质要求", "quote_sha256": "95b3527db3017bf77ea5e3b2d688d50a9abac774b2abb3d5e9db40514f73be35", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-06/05-lie-algebras-and-lie-groups", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-429f631b8b462d8f5de6455c" }, { "concept_id": "urn:uuid:7c7d436a-933b-40b7-9fbb-45f0ff035eec", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-06/05-lie-algebras-and-lie-groups", "anchor": "first-b678679c2e7f94246618-en", "chapter": "6", "section": "6.5", "offset": 16000, "range": [ 22579, 22820 ], "source_revision": "0c41f9583a4efa9fbdd777c6458b2ae3bc19756b6ad688f6ce8a74bf16814ed7", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "one-parameter subgroup", "context": { "range": [ 22577, 23238 ], "quote": "A one-parameter subgroup of a Lie group $G$ is the image $\\varphi ( \\mathbb { R } )$ of a homomorphism $\\varphi : \\mathbb { R } \\to G$ of the additive group of real numbers into $G$. 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