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[2607:f8b0:4864:20::12e]) by gmr-mx.google.com with ESMTPS id i12-v6si793218plt.5.2018.10.29.19.02.53 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Mon, 29 Oct 2018 19:02:53 -0700 (PDT) Received-SPF: pass (google.com: domain of josephcmac@gmail.com designates 2607:f8b0:4864:20::12e as permitted sender) client-ip=2607:f8b0:4864:20::12e; Received: by mail-it1-x12e.google.com with SMTP id e81-v6so11668418itc.1 for ; Mon, 29 Oct 2018 19:02:53 -0700 (PDT) X-Received: by 2002:a24:9302:: with SMTP id y2-v6mr113943itd.49.1540864972356; Mon, 29 Oct 2018 19:02:52 -0700 (PDT) MIME-Version: 1.0 References: <1627abd4-4ab6-48f3-bd7c-0035d8434c74@googlegroups.com> In-Reply-To: <1627abd4-4ab6-48f3-bd7c-0035d8434c74@googlegroups.com> From: =?UTF-8?Q?Jos=C3=A9_Manuel_Rodriguez_Caballero?= Date: Mon, 29 Oct 2018 22:02:41 -0400 Message-ID: Subject: [HoTT] Quantum Groups To: HomotopyTypeTheory@googlegroups.com Content-Type: multipart/alternative; boundary="00000000000053077d0579689581" X-Original-Sender: josephcmac@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; dkim=pass header.i=@gmail.com header.s=20161025 header.b="G/yAmTgG"; spf=pass (google.com: domain of josephcmac@gmail.com designates 2607:f8b0:4864:20::12e as permitted sender) smtp.mailfrom=josephcmac@gmail.com; dmarc=pass (p=NONE sp=QUARANTINE dis=NONE) header.from=gmail.com Precedence: list Mailing-list: list HomotopyTypeTheory@googlegroups.com; contact HomotopyTypeTheory+owners@googlegroups.com List-ID: X-Google-Group-Id: 1041266174716 List-Post: , List-Help: , List-Archive: , --00000000000053077d0579689581 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Hello, Roughly speaking, a quantum group is an algebraic structure which is obtained by means of a deformation of a group. There rigorous definition is here: https://ncatlab.org/nlab/show/quantum+group Official reference to quantum groups: Kassel, Christian (1995), Quantum groups, Graduate Texts in Mathematics, 155, Berlin, New York: Springer-Verlag, doi:10.1007/978-1-4612-0783-2, ISBN 978-0-387-94370-1, MR 1321145 Deformations... homotopy type... Well, given a "well-behaved" family of quantum groups, which are deformations of the same group, is it "natural" to define this family as a homotopy type? Is HoTT, in some way, a natural setting to work with quantum groups because types and homotopy types are identified? Kind Regards, Jos=C3=A9 M. --=20 You received this message because you are subscribed to the Google Groups "= Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an e= mail to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. --00000000000053077d0579689581 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Hello,
=C2=A0 Roughly= speaking, a quantum group is an algebraic structure which is obtained by m= eans of a deformation of a group. There rigorous definition is here: https://ncatlab.org/nlab/= show/quantum+group

<= div>Official reference to quantum groups: Kassel, Christia= n (1995), Quantum groups, Graduate Texts in Mathematics, 155, Berlin, New Y= ork: Springer-Verlag, doi:10.1007/978-1-4612-0783-2, ISBN 978-0-387-94370-1= , MR 1321145

Deformations... homotopy type... Well, given a "well-behave= d" family of quantum groups, which are deformations of the same group,= is it "natural" to define this family as a homotopy type? Is HoT= T, in some way, a natural setting to work with quantum groups because types= and homotopy types are identified?

<= /font>
Kind Regards,
Jos=C3=A9 M.


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