{"product_id":"property-t-for-groups-graded-by-root-systems","title":"Property ($T$) for Groups Graded by Root Systems","description":"\u003cp\u003eThe authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003eAuthor:\u003c\/b\u003e Mikhail Ershov, Andrei Jaikin-Zapirain, Martin Kassabov\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublisher:\u003c\/b\u003e American Mathematical Soc.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublished:\u003c\/b\u003e 2017-09-25\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePages:\u003c\/b\u003e 148\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Soc.","offers":[{"title":"Default Title","offer_id":62811926790515,"sku":"9781470426040","price":200.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0987\/0812\/8115\/files\/content_d69bda3c-9c1e-4d71-b684-8458a08ba925.jpg?v=1778043839","url":"https:\/\/readaura.store\/products\/property-t-for-groups-graded-by-root-systems","provider":"Read Aura","version":"1.0","type":"link"}