{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"2657a410-20c6-5599-bf5a-f35830756e11","task_key":"test--2657a410-20c6-5599-bf5a-f35830756e11","task_revision_id":"1","upstream_id":"","short_description":"For any $n \\geq 1$, let $A$ denote the $\\mathbb{C}$ algebra consisting of $n…","config":"","split":"test","body":"{\"problem\":\"For any $n \\\\geq 1$, let $A$ denote the $\\\\mathbb{C}$ algebra consisting of $n \\\\times n$ upper triangular complex matrices $\\\\left\\\\{\\\\left(\\\\begin{array}{ccc}* & * & * \\\\\\\\ 0 & * & * \\\\\\\\ 0 & 0 & *\\\\end{array}\\\\right)_{n \\\\times n}\\\\right\\\\}$. We shall consider the left $A$-modules (that is, $\\\\mathbb{C}$-vector spaces $V$ with $\\\\mathbb{C}$-algebra homomorphisms $\\\\rho: A \\\\rightarrow \\\\operatorname{End}(V))$. (2) Determine all simple modules of $A$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}