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For G = SU(n), Sp(n) or Spin(n), let be the centralizer of a certain SU(2) in G. We have a natural map . For a generator α of , we describe J⁎(α). In particular, it is proved that is injective.
Yasuhiko Kamiyama. "Generating varieties for the triple loop space of classical Lie groups." Fundamenta Mathematicae 177.3 (2003): 269-283. <http://eudml.org/doc/282803>.
@article{YasuhikoKamiyama2003, abstract = {For G = SU(n), Sp(n) or Spin(n), let $C_\{G\}(SU(2))$ be the centralizer of a certain SU(2) in G. We have a natural map $J: G/C_\{G\}(SU(2)) → Ω₀³G$. For a generator α of $H⁎(G/C_\{G\}(SU(2));ℤ/2)$, we describe J⁎(α). In particular, it is proved that $J⁎: H⁎(G/C_\{G\}(SU(2));ℤ/2) → H⁎(Ω₀³G;ℤ/2)$ is injective.}, author = {Yasuhiko Kamiyama}, journal = {Fundamenta Mathematicae}, keywords = {generating variety; instantons; triple loop space}, language = {eng}, number = {3}, pages = {269-283}, title = {Generating varieties for the triple loop space of classical Lie groups}, url = {http://eudml.org/doc/282803}, volume = {177}, year = {2003}, }
TY - JOUR AU - Yasuhiko Kamiyama TI - Generating varieties for the triple loop space of classical Lie groups JO - Fundamenta Mathematicae PY - 2003 VL - 177 IS - 3 SP - 269 EP - 283 AB - For G = SU(n), Sp(n) or Spin(n), let $C_{G}(SU(2))$ be the centralizer of a certain SU(2) in G. We have a natural map $J: G/C_{G}(SU(2)) → Ω₀³G$. For a generator α of $H⁎(G/C_{G}(SU(2));ℤ/2)$, we describe J⁎(α). In particular, it is proved that $J⁎: H⁎(G/C_{G}(SU(2));ℤ/2) → H⁎(Ω₀³G;ℤ/2)$ is injective. LA - eng KW - generating variety; instantons; triple loop space UR - http://eudml.org/doc/282803 ER -