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• W2974543293 abstract "Abstract The group algebras <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>Q</m:mi> <m:msup> <m:mn>2</m:mn> <m:mi>n</m:mi> </m:msup> </m:msub> </m:mrow> </m:math> {kQ_{2^{n}}} of the generalized quaternion groups <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>Q</m:mi> <m:msup> <m:mn>2</m:mn> <m:mi>n</m:mi> </m:msup> </m:msub> </m:math> {Q_{2^{n}}} over fields k which contain <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>𝔽</m:mi> <m:msup> <m:mn>2</m:mn> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:msub> </m:math> {mathbb{F}_{2^{n-2}}} are deformed to separable <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>t</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {k((t))} -algebras <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow> <m:mo stretchy=false>[</m:mo> <m:mrow> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>Q</m:mi> <m:msup> <m:mn>2</m:mn> <m:mi>n</m:mi> </m:msup> </m:msub> </m:mrow> <m:mo stretchy=false>]</m:mo> </m:mrow> <m:mi>t</m:mi> </m:msub> </m:math> {[kQ_{2^{n}}]_{t}} . The dimensions of the simple components of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mover accent=true> <m:mrow> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>t</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>¯</m:mo> </m:mover> <m:msub> <m:mo>⊗</m:mo> <m:mrow> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>t</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mo stretchy=false>[</m:mo> <m:mrow> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>Q</m:mi> <m:msup> <m:mn>2</m:mn> <m:mi>n</m:mi> </m:msup> </m:msub> </m:mrow> <m:mo stretchy=false>]</m:mo> </m:mrow> <m:mi>t</m:mi> </m:msub> </m:mrow> </m:math> {overline{k((t))}otimes_{k((t))}[kQ_{2^{n}}]_{t}} over the algebraic closure <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mover accent=true> <m:mrow> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>t</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>¯</m:mo> </m:mover> </m:math> {overline{k((t))}} , and those of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>ℂ</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>Q</m:mi> <m:msup> <m:mn>2</m:mn> <m:mi>n</m:mi> </m:msup> </m:msub> </m:mrow> </m:math> {mathbb{C}Q_{2^{n}}} over <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>ℂ</m:mi> </m:math> {mathbb{C}} are the same, yielding strong solutions of the Donald–Flanigan conjecture for the generalized quaternion groups." @default.
• W2974543293 created "2019-09-26" @default.
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• W2974543293 date "2019-09-18" @default.
• W2974543293 modified "2023-09-23" @default.
• W2974543293 title "Separable deformations of the generalized quaternion group algebras" @default.
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